F-droid is repository for Android that distributes FOSS apps built from source.
Twimight can't be included because keys must be included in the source for it
to build, which Twitter doesn't like. Apps have got around this in different
ways: ROT-13 obfuscation, sweetheart deals in the case of Gwibber on Ubuntu.
Another way would be to alow the app to build without keys and to provide an
interface to put one's own keys into: it isn't actually difficult to obtain
one's own keys from Twitter.