I have no experience of growing in Florida, Lmck, but alliums love to grow in a 'mediteranean climate', ie with a hot, dry summer - I think that you can manage that!

Well they grow in California! Certainly the American species do at least. Check out this American site with a massive amount of info on American species plus all the others too.
http://www.plantbuzz.com/allium/Allium.htm

Many from both principle sections of the genus should do pretty well, even the fussy types that have rhizomes rather than bulbs.

I think your best bet, Lmck, is to find a local nursery and pick their brains! Also, take a look in local gardens and see what grows best.

The heat and high humidity of summer, and the lack of chilling, will probably preclude some species, such as A. caeruleum, and A. moly. The giant ones are going to be iffy--look for the ones more consistently listed for USDA zone 9, as opposed to zone 8. Low elevation Mediterranean species, such as A. neapolitanum, and A. pulchellum, are probably going to be among your best bets. My favorite for ease of culture is A. tuberosum (Garlic Chives), though I wish the flowers came in some color other than white!

yes they do. I live in East Central Florida Zone 9 and they grow and multiply - they only bloom once a year. Today is June 29, 2011 and one just finished and the other just bloomed out today.