I'll kick this off by saying that Johan Cruyff is my favorite player ever, so I'm not exactly unbiased in trying, however tenuously, to assign Fiorentina to his legacy. There are better-written and better-informed elegies to his genius available elsewhere (or just go to YouTube and watch the hours of footage available there, because they're all worth it), so I'm not going do that. Rather, and although there's no obvious connection between him and Florence, I want to show that, out of all the Italian clubs, Fiorentina has embraced most closely his beliefs on how the game ought to be played.
At this point, everyone knows what Total Football is. While it's maybe a little reductive to say that Cruyff (and Rinus Michels) developed the whole thing--Victor Maslov certainly deserves a nod--but if you look at what the system was originally designed to do, it's astonishingly similar to how Fiorentina have set out for the past half-decade.
Fiorentina under Montella (and Paulo Sousa, for that matter) have placed great emphasis on possession. While this isn't a necessarily Cruyffian tactic--keeping that ball has been a viable strategy for a century--the quick passing, especially out from the back, has always been one of his points of emphasis. More to the point, the idea to fill attacking roles with players who are nominally central midfielders (Borja Valero, Matías Fernández) or who tend to drop back into the midfield (Josip Iličić), Fiorentina have attempted to foster the position-switching so crucial to Total Football by encouraging deeper midfielders and wingbacks forward as attackers drop back.
The other area in which Cruyff's fingerprints are all over this team is in their pressing. Fiorentina generally keep a very high defensive line, looking to squeeze opponents off the ball by limiting the area they can play in. This most Dutch application of space must be matched, of course, by high defensive pressure in the midfield and from the forwards. While the Viola only sporadically press up the pitch, they do tend to hunt down the opposition with the ball a few times a game, especially in "big" matches, just as Cruyff instructed his Ajax and Barcelona teams to do.
Obviously, these aren't particularly unique traits for a modern team to demonstrate, but this only goes to show how expansive and complete Cruyff's vision of the game was. In personality, too, he resembles Fiorentina: brilliant but enigmatic, capable of the sublime and the inexplicable, the neutral's favorite but never quite able to put it all together on the biggest stage. As someone who completely rethought the landscape of how the game works, too, it's not absurd to equate him with the birthplace of the Renaissance. And if that doesn't make sense, well, "If I wanted you to understand, I would have explained it better."