Not sure why you planned it so tight - a last-minute trip? Looks like you aren't going to get a lot of sleep that first night - which is the last thing I'd personally want to do after flying from overseas(?).
I DOUBT you'd make the last good direct train at 8:50PM to Florence leaving out of Rome, if you take a taxi to Rome Termini station from the airport. Your only shot is no checked bags, hope your flight is on time, and lines at immigration are short when you arrive. Then again, if you are flying in from elsewhere in Europe(?), you won't have to go through immigration upon arrival. Customs is probably a 10 second walk past the customs agent at baggage claim if, like most people, you have nothing to declare.
But I wouldn't count on making that 8:50 train.
Other public transit options are: train leaving at 10:35 with a change, get in to Florence at 2:19.
Or FlixBus: 10:45 from Rome, get in at 1:50am (no changes at least).
Or stay over in Rome - you'll probably be exhausted upon arrival anyway - and take the early 5:45am Italo train from Rome gets to Florence at 7:17. Leave your bags at the station if you have to if you are coming back to Florence in the evening.
These all seem like bad options but given those parameters, I don't see a good one.
Or...hire a private transfer to pick you up directly at the airport, probably not cheap, to get you to Florence that same evening.