The only example I've seen so far is The Rapper's Flow Encyclopedia, which uses standard musical notation with phrasing to indicate cadence, and lyric capitalization to indicate (but not group) rhymes. [Migrated from musicfans SE.]
I know little about rap. But just from pure logic and having played music...
There are only 2 musical notation systems - standard notation and piano roll notation. There's no melody involved in most rap (which I just don't get, but that's beside the point).
Either system will work perfectly well.
Rap is just music. Use whatever music notation you like. Or none like I suspect a lot of rappers do.
Once it's recorded, slow it down and pick out the rhythm. It's much easier than trying to pick out rhythm, bass, melody, and chords. A recording of rap is very close to notation.