A type of bazaar where inexpensive goods are sold or bartered.
A flea market has a wide variety of items available, things such as fresh foods, 
worn clothes, furniture, and more. People go to these markets to exchange 
goods, either by buying, selling, or even bartering for an item.

Flea markets are oftentimes located outdoors in large fields or under big tents. Since they take place outside, it's possible for insects, like fleas, to get on not only the items being sold, but the people who are attending. On that note, according to Wikipedia, one of the theories as to where this phrase originates from is the French 'marché aux puces', which literally translates to 'market where one acquires fleas.'

One of the oldest and most popular flea markets is located in Paris, France, and it has held the name Les Marché aux Puces (the flea market) since around the 1870s. Thus the term is at least that old.
Common Phrase Origins and Meanings  |  F-Letter Expressions
Note: For most of the common expressions, sayings, and idioms, finding where they originated exactly is nearly impossible. Normally what's provided is around the oldest time a phrase was recorded in a book, poem, or play. Sometimes, there will be an early printed use of a phrase in an old newspaper, which will often be quoted to give you an approximate age for the saying.

However, it should be noted that if a certain idiom is being used in a form of media, like a newspaper, then it's probably already a commonly known saying, thus, it should be assumed that the phrase origins are probably from an older time.
KnowYourPhrase.com - Meanings and Origins of Phrases
* Later today we are going to the flea market and you are welcome to join us if you'd like.

* I'm going to stop by the flea market that's in town to try and sell some of the junk that's taking up space in our garage.
Flea Market phrase meaning.
Origins for the idiom Flea Market.
A list of phrases starting with the letter - F.
Phrases and Idioms