Since you arrive in Florence in the afternoon, you'll miss the "artsy and antique-y" stands at the Tuesday market in Cascine Park (8am-2pm). The only ongoing market I can think of in Florence with those types of items is the one in the piazza behind the Sant'Ambrogio Market. It's the same small market that used to be in Piazza dei Ciompi, which is currently undergoing construction. Also, a few of the stands outside the Sant'Ambrogio Market sell small antique items. I'd suggest going later in the morning when the Market is still going strong and the stands behind it are more likely to be open. The Market closes around 2pm, with some stands starting to pack-up around 1:30.
Edit: The name of the market behind Sant'Ambrogio Market is Mercatino delle Pulci, although Google lists it as Mercato delle Pulci. It opens later and also closes later than the Sant'Ambrgio Market.