We are working on implementing Flex with callback and voicemail functions, as documented in: https://www.twilio.com/docs/flex/solutions-library/queued-callback-and-voicemail
Its quite close to what we want, but we would like to be able to access voicemail messages even after an agent handled the task, and the task was completed. I can't seem to find where those recordings can be available from?
In that plugin, the voicemail audio URL is attached to a Task's attributes. According to the TaskRouter documentation on the lifecycle of a Task, once a Task has reached a terminal state (canceled or completed) it is deleted 5 minutes later).
So, you cannot retrieve the voicemail URL from the task.
Call recordings are available through the Twilio REST API though. If you wanted to build a page in Flex that listed the call recordings that have been left as part of this workflow, you could, for example, fetch the recordings from the API (using a Twilio Function) and render them into the Flex page.
That will give you the recordings without any metadata though. If you need to store the metadata further, you will likely need to dig further into the queued callbacks and voicemail plugin to find somewhere to store the data in your own permanent store.