It is definitely a Louisiana iris, which should do really well in Florida. Make sure to keep it well watered. And, unlike bearded iris, you should mulch it to help keep it moist.
Black Gamecock is a popular iris and grows more places than most. On looking into Black Gamecock it looks like yours has the correct triangular form as compared to the cartwheel form in the database picture. The American Iris Society (AIS) database doesn't shed more light on this difference because there are pictures with all sorts of different shapes. I wonder if anything with that coloration was given the same name, but may actually be two or more different iris. Anyway, it is pretty safe to call yours Black Gamecock. To be absolutely sure though you should order one and compare them.