From the official Calcio Storico site -
Biglietti edizione 2018
L'acquisto dei biglietti per le partita finale del Calcio Storico Fiorentino potrà avvenire, a partire dalle ore 11 del giorno martedì 19 giugno p.v., esclusivamente presso la sede del Box Office, via delle Vecchie Carceri 1 Firenze, con pagamento digitale tramite bancomat, carta di credito (con esclusione del circuito AMEX) e carta prepagata.
This means that you can ONLY buy tickets from the Box Office in Florence.
Yep, this year the city decided to make it possible to only buy tickets by going in person to Box Office Toscana's main office on Via delle Carceri a few days ahead of the matches.
So tickets for the final this Sunday can be purchased starting today, for the semifinals they started 3 days before.
A lot of people have complained so let's see how it goes overall and whether they change it back next year, it makes no sense that you can't buy online in today's technological world (it was, of course, intentional).
What many forget is that the Calcio Fiorentino (and the Palio of Siena) are, despite the presence of many tourists, fundamentally local events woven into the history of the two cities and still VERY important locally.
My suspicion is that today's technologies high-jacked the sale of tickets (Viagogo, Ticketmaster etc etc) denying locals of tickets or at least at fair prices.
So maybe the decision to limit sales to the local box office has sense.