Poet Assistant! It's a dictionary app that offers:

• a rhyming dictionary, using the Carnegie Mellon University pronunciation dictionary.

• a thesaurus, using the WordNet thesaurus.

• a dictionary, using the WordNet dictionary.

• a screen where you can enter your poem text, and have it read aloud back to you by the device's text-to-speech engine.

Poet Assistant works offline, without any internet connection.

F-Droid | Github

Initial attempts to search for this were frustrated because my search engine kept trying to find rhymes for "FOSS" or "Open Source"

However, I did find an app with credits that showed what libraries it used.

In particular, this one might be up your alley: Carnegie Mellon pronouncing dictionary. It looks like you'd still have to combine it with an existing dictionary in order to find the rhymes, but at least you can get the pronunciation

This might be helpful for development:

https://archive.org/details/mobypronunciatio03205gut

Levenstein the app?