How to make a flex child overflow its parent as it grows?

I have a flexbox with a single flex child:

<div class="flex-parent">
  <div class="flex-child">
    lots of content...
  </div>
</div>

.flex-parent has a fixed size:

.flex-parent {
  height: 250px;
}

The flex child has so much content that it should overflow the size of its parent. Instead, its height stays "capped" at the height of the parent (250px).

How can I fix this and make .flex-child grow with its content? I can easily fix it by switching to display: block but my real layout is much more complicated which makes that impractical.

The problem: http://codepen.io/anon/pen/OWjYwe
How it should work: http://codepen.io/anon/pen/apyraV

Solution

The use of flex on a box with a single child might be useless unless for vertical/horizontal alignement.

To allow the flex-child to grow hover the setted height, then reset flex-direction to column:

see answer of @Michael B for details about flex item sizing algorithm

.flex-parent {
  display: flex;
  height: 200px;
  flex-flow: column;
  border: solid;
}
.flex-child {
  background: cornflowerblue;
}

<div class="flex-parent">
  <div class="flex-child">
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content
  </div>
</div>
<p>What about me ?</p>

You may also use overflow but different behavior:

.flex-parent {
  display: flex;
  height: 200px;
  overflow:auto;
  border:solid;
}

.flex-child {
  background: cornflowerblue;
}

<div class="flex-parent">
  <div class="flex-child">
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
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    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content
  </div>
</div>
<p>What about me ?</p>

Finally, use min-height instead height

.flex-parent {
  display: flex;
  min-height: 200px;
  border:solid;
}

.flex-child {
  background: cornflowerblue;
}

<div class="flex-parent">
  <div class="flex-child">
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
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    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content content
    content content content content content content content content content content content content content content content content content content content
  </div>
</div>
<p>What about me ?</p>