Two theories: The first `flea market' may have been New York's raucous Fly Market, a fixture in Lower Manhattan from before the American Revolution until around 1816, the `Fly' came from the Dutch name for the market, `Vly' or `Vlie,' which meant `valley,' and was pronounced, you guessed it, `flea.' Voila, `flea market.' Maybe.The other -- and most likely -- theory, originates in Paris, where Le Marche aux Puces ("market of the fleas") was an early version of the outlet shopping mall. The market took its name from the partly humorous, partly accurate assumption that the market's ragtag goods more than likely were infested with fleas. The phrase "flea market" first appeared in English in the 1920s and probably was a simplified translation of the French market's name.
these were sheds that used to store imported wood and fleeces, which were then sold on to the public, obviously these fleeces and wood contained all types of insects so these sheds were commonly known as fleamarkets.