I don't like the Kindle app on Android. At least I didn't like it the last time I tried it which was years ago, it may have gotten better. They make it extremely difficult to find the local files related to the books in the in-app library, or bookshelf or whatever they call it. Those files might only be available on the cloud for that matter.
I've been using FBReader for a lot of years. It has built-in access to online network libraries, including Project Gutenberg. I don't really use them though. I usually download an e-book to my phone then open it in FBReader from the file system. It does .epub, mobi, pdf, probably many others.
There are other free e-reader apps out there as well. I've tried a couple and always came back to FBReader.