I don't have any beta on Pensacola specifically, but everywhere around there seems to be good for kiting. I grew up in Alabama an hour east of Pensacola and I take my gear home whenever I visit. It's always windy somewhere near there around the holidays. The great thing about the area too is with all the barrier islands around you can usually find somewhere that a particular wind direction works. I've kited mostly in Mobile Bay and messed around in the gulf near Gulf Shores, but I know people used to kite at a park near the Florida border. I know they had banned kiting in the park at some point because they thought it was disturbing birds or something. Hopefully that has changed now. Navarre Beach is also really good and is really close to Pensacola.
I would think that the summer would be pretty dead, but the rest of the year should be good. Check http://www.fksa.org/
I believe there is a shop in Pensacola also.
One last thing. At least in my hometown on Mobile Bay, kiting hasn't really caught on yet so there's some pretty epic spots that no one goes to.