who says a funk band can't play rock?

I'll second the James Brown and P. Funk suggestions as great starting places for the funk. They are very different so be sure to check them both out!

I see some new stuff in your list Zola, thanks for that!!

Stanley Clarke is a great bassist and has some really funky tracks. I enjoy School Days and the Bass-ic Collection.

Herbie has been known to get down.

For some newer stuff:

Perhaps one of my favorite local treats is Antibalas Afrobeat Orchestra. I'd guess this would primarily be called Afrobeat but I think the funk is undeniable in the majority of their tunes. There is no bad starting place for them, my personal favorite is the 12" with Ticklah but I don't think this is the most accessible.

John Hickey Band is a band I've seen open for P. Funk on a couple occasions. Fun, solid, catchy grooves.

Satchmo nailed the big ones I'll add:

Curtis Mayfield
Prince
Funk Inc. (although leaning a bit more towards the jazzy side despite the name)

The Headhunters album "Survival of the Fittest", why was it not released until the 2000's when it was recorded in the 70's?

For that specific album, I don't know, but there are several occasions of such weirdness across genres. Similarly John Lee Hooker's Burning Hell didn't see a US release until years after it was legendary in Europe.