You can grab the RSS feed from LibriVox and put it into most podcast apps.

I'm on iOS and really enjoy using Overcast.

Archive.org has a pretty easy interface. I prefer it over the Android apps I've tried, because I can easily move to desktop using synced browser data, or send books to other devices. Example:

https://archive.org/details/scaramouche_gm_librivox/

The mobile site is actually half-decent. You can download the MP3s and listen to them in something like VLC as well.