Can anyone provide me with working example how to show analytics (Visits, Page views, Page views per visit, etc) for logged users? As I understand there is no OOB solution, so I've tried to implement flexible dimensions, but didn't find any good examples and failed.
First of all you have to identify your logged in contact by calling the Sitecore.Analytics.Tracker.Current.Session.IdentifyAs() method, see more details here. When the contact logs in you can use their username to identify them upon the successful login.
Note, that the identification and authentication are separate unrelated events. Contacts are identified against the xDB and authenticated against the authentication mechanism used by the website.
When the contact identifies, it is saved to xConnect with a known identifier based on the information passed into theIdentifyAs() method: Identifier, Source and
IdentifierType will be set to ContactIdentifierType.Known (it is set to ContactIdentifierType.Anonymous for anonymous contacts). Then you can use IsKnown property on the Sitecore.XConnect.Contact that returns true if a contact has any known identifiers.
If you want to track some custom events for the logged in users to then use them for reporting needs you can add user interactions by calling the client.AddInteraction() extension method. I have given an example here.
If you want to extend the contact with your own custom data then you can create custom contact facets, read more here.
In order to implement your custom report with flexible filtering by logged in and not users, of course, you will need to define your custom dimensions and metrics, read more here.