Florence taxi cab payment

It depends. They should but sometimes the machine isn't working. And sometimes your card might not work either. Just be prepared to pay cash and if the credit works consider it a bonus. Always ask prior to getting into the taxi. And have a second card available or cash should your card get funky.

They do accept credit cards, however sometimes (but not often in my experience) they find the excuse that their POS machine isn’t working that day.
99.9999% of the times it is a lie. A credit card payment is traceable by the tax authorities, whereas a cash payment can be easily go unreported to the tax man to avoid both the 22% of VAT (which you pay as it is included in the fare, but that the cab driver owes the State) and also to underreport their income for income tax purposes.
The taxi fare from FLR to anywhere in the city center is a flat fare of about 24€ plus 1€ per bag (a bit more at night from 10p to 7am and on Sunday). If you must pay by credit card, ask if the POS machine works before boarding, if they tell you no, then respectfully decline and go to the next cab. Rest assured that at the prospect of losing your business all of the sudden his machine will start working.