Cell phone companies base their tax rates on your billing address generally, not on your phone number. Unless you've somehow not changed your billing address, you're paying Florida taxes and fees already, and switching to a new Florida based phone won't affect that. (Florida has cell phone taxes that are among the highest.)
The only way I know of to avoid them (or, more precisely, avoid dealing with them directly, as doubtless you're still paying them somehow under the covers) is to use a prepaid cell phone service like Tracfone, Net 10, Straight Talk, etc. The only extra tax you have to pay explicitly with them is any ordinary sales tax on the purchase of minutes.
