I saw this a few days ago in F-Droid's „Recently Added“ category, a bluetooth chat app called Gilgamesh:

https://github.com/n8fr8/gilgamesh (https://f-droid.org/repository/browse/?fdid=info.guardianpro...)

Don't know if it's anonymous or encrypted (is that is even possible?) but other then Firechat (and most other apps linked here until now) it's Open Source.

Would love to know what someone with a more technical expertise than me thinks about this.