There are two theories about the origin of "flea market," and although I'm fairly certain that one of them is actually a case of linguistic coincidence, we'll take them both for a spin. According to etymologist Christine Ammer, 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.
However, while the Fly Market certainly existed, and its name was evidently indeed pronounced "flea market," the actual origin of the term most probably lies in Paris, where Le Marche aux Puces (literally, "market of the fleas") was a popular shopping venue. Le Marche aux Puces took its name, as you might have guessed by now, from the semi-humorous (and probably at least partly accurate) popular perception that the market's ragtag goods were more than likely to be infested with fleas.
In any case, "flea market" first appeared in English in the 1920's and is most likely a simple translation of the French market's name. If "flea market" had gained currency from the Manhattan "Fly Market," it almost certainly would have appeared in print much earlier than it did.