Matheson Hammock Park has great flat water, heaps of space and an awesome view. Just the launch is a bit dodgy since there is no beach. You set up at the car park.
http://www.kitebeaches.com/kitesurf/loc/matheson_hammock_park.htmlCrandon Park is a good spot as well (bit more choppy), but you gotta pay a fee (25 bucks or so) to kite there.
www.kitebeaches.com/kitesurf/loc/crandon_beach_park.htmlWhen kiting Fort Lauderdale, I wouldn't ride too far out - Florida is the shark capital of the world, especially July-December there could be hundreds, although they are usually just small buggers.
Overall, Florida is quite conservative and folks have serious trouble with spots getting closed etc. So play by the rules, only kite within the buoys etc.