Get a lawyer if you like wasting money, otherwise..............
Establish residency by
Filing a declaration of domicile
File that with the county clerk.
After that, all you need to do is fill out this
form and take to County Tax office along with your VA Letter.
The above assumes that you already have registered to vote, obtained a Florida drivers licence and registered your vehicles here.
Your mortgage company is still going to require you pay tax money into escrow, but will refund and adjust monthly payment after they receive the tax bill.