I was quite disappointed to see that Meridiana Airlines has suspended its non-stop flights between Florence and Palermo effective October 1.
Meridiana continues its air service to Catania, and flights to Palermo continue out of Pisa Airport on both Windjet and Ryanair (the latter having fares as low as 11 Euros).
Travellers wishing to fly from Florence to Palermo are best advised to use Pisa Airport. Otherwise, Alitalia has connecting flights via Roma Fiumicino (but this option is much more expensive). Flying Meridiana into Catania would then require taking the hourly direct bus to Palermo from the Catania Airport, but that is a 2.5 hour bus trip, making it a less attractive travel option. There are also flights from Bologna to Palermo, but this is not as convenient (or as cheap) as flying out of Pisa.
Much slower options from Florence to Palermo include taking the direct overnight train (not particularly recommended), a morning train (connecting to the "Archimede" IC train at Roma Termini), or an early afternoon train to Naples, connecting to the overnight Tirrenia or SNAV car ferry.
I think that Florentines will miss this direct flight. It is unknown at present whether the service will be resumed next summer.