Not sure I understand but let's see - you want to know of flea markets in Florence so that you can go see if you can find ceramic tiles to get inspiration for a restaurant decor/design?
The truly difficult part about replying is that you are coming in August, when the temps get warm and lots of people close shop and head on vacation. Lots of the outdoor markets (not just flea) that take place in Florence every month throughout the year take a break in August. So I can only tell you of when two of Florence's main flea markets would usually run if they were to follow the normal schedule - but cannot guarantee that they will be there!
Fortezza Antiquaria - 3rd weekend of the month, in August that would be teh 15th-16th... BUT as the 15th is a national holiday on top of it being August - I highly doubt this will be taking place.
Piazza dei Ciompi - last Sunday of the month is the big flea market around the Piazza --- you won't be here then, but I am telling you about it since there are small antique shops in the Piazza that are there every single DAY. I think this is your best bet to head to, hoping they aren't closed for the holidays.
Sorry to give bad news ---- if that is what your question was ;-)!