While you do not need a license for an Uzi (which is not considered a "concealed weapon), if it is fully automatic (hold the trigger and it continues to fire) you DO need a license from the U.S. Bureau of Alcohol, Firearms and Tobacco to own that Uzi. If it was the commercially available semi-automatic (one trigger pull, one shot) and you want to carry it concealed, yes, you will need a Florida concealed weapon permit (although why you would want to carry something so large and awkward puzzles me.)
