Sounds like you want a podcast app. Pocket Casts can do all these things. (Cloud upload needs a Plus subscription, though. But you could also self-host your own RSS feed with your files.)
> But you could also self-host your own RSS feed with your files.
That is a brilliant idea and now I want to do this!
I already have a little PHP script that makes an RSS feed out of any txt files it finds in the same folder, it should be easy to switch to a podcast feed...
