I find audiobooks on the Internet and download the files locally to my device, then I play them with Voice audiobook player. Audiobookbay has lots to download, but you have to make an account.
Above board? There is an app that lets you connect with the local library where you can "borrow" audiobooks. Check your local library for what app to use.
Below decks? I'm not sure, but One-Piece is pretty neat.
It's called Libby. You can plug in multiple library cards too, which is cool since some library systems have more stuff. Poke around and you can find some big libraries that let you get a card online without ID or (rigorous) proof of residency.
i'm using VLC player right now, i'm sure there's more efficient ways, but i already had it for other stuff and it always remembers where you paused, even after you've moved on to other files. i literally just drag and drop mp4 files into my sd card and VLC has always been able to find them automatically
There's a pretty comprehensive pile of audiobooks available on TankieTube, mostly theory and some bios and history, now. In particular check out Communist Broadcasting Service and Book Broadcasting Channel. More will be added in the coming weeks.
You can use the app GrayJay to access TT via android app if you'd prefer that over using a web browser, which might get buggy with the screen off or whatever. Here's a guide I made on how to add TT to GrayJay: