Flight to Rome delayed - how to get to Florence?

There are constant trains from Rome to Florence, but you would need to get from the airport in Rome to the train station in Rome and then from train station in Florence to the airport in Florence(which isn't difficult or expensive).

The luggage would be my concern assuming you can't ask for it back. Otherwise I'd take the train.

I would first talk to ITA. It is not clear whether you have checked in and no longer have your bags, are in Rome, or what stage of the journey you are at.

But if you talk to ITA, they may be able to pull your bags for pickup in Rome, then just take the train, simple to get from The airport to Termini (Leonardo Express) then trains nearly every half hour or so to Florence, probably get there quicker than you would have by plane.

Quick and easy once in Florence to go out from the train station to its very nearby airport. Or take a taxi from your hotel or apartment, since you might beat your luggage to Florence.

But would their luggage get to Florence if they abandon their connecting flight? If they are a no show at the gate, wouldn't their luggage have to be off loaded?

I agree with the advice to first check with ITA airlines. If the bags are already out of your possession and checked through to Florence, you may be able to ask once you arrive in Rome what your options are. In the past I’ve had my luggage delivered to my hotel at no cost to me. Granted my circumstances were not the same as yours, I thought it was worth sharing in the event this may be an option for you.
Since the delay is no fault of your own, they may be willing to deliver the luggage to your hotel if you indicate upon arrival in Rome you will be taking alternate transportation to florence due to having missed your connection as a result of the delay. The downside to this is the luggage may take longer to arrive at your hotel, so if a day without your luggage may present an issue for you then better to pickup from Florence airport.

You could even ask ITA to get you a train ticket... I'm a bit puzzled that there are still Rome - Florence flights...

It appears OP was in ATH when he wrote about the 3 hour delay of the flight to FCO.

Having already checked bags, the tricky part ( logistics) would be retrieving the bags at FCO and then taking a train as presumably the last flight to Florence left before his arrival.

Hopefully when things are no longer in crisis mode OP will have the time to let us know what happened.

Thank you all for the ideas and suggestions. WE MADE IT TO FIRENZE! We had to run through the airport, but ITA held the plane a good while for us (and a number of other people arriving late).

Who knows about our bags, but we’re glad to be here!! :)

Mama Mia!

Thanks for reporting back. Glad you made it. What a day!