This will all be very platform specific stuff.
Start here:
It might be integrate-able with Unity as a plugin or library, or even directly with the Android classes.
Let me also warn you before you go too far down this rabbit hole: making any kind of background app in Unity is going to have all kinds of performance issues.
Unity is really engineered first and foremost as a high performance graphics presentation mechanism.
Even a Unity app in the background rendering nothing at all on the screen is going to probably burn 100x or even 1000x the amount of battery life as the typical audiobook application, which will just barely sip battery juice.
If you feel like making an audiobook app, just do it in native Android already, otherwise it will burn through battery power incredibly fast.