One of the easiest ways to get a better price at a flea market is to buy more than one thing from the same vendor. Vendors would generally rather sell several items at a slight discount than a single item at full price, and a bundle gives you leverage you do not have on a single purchase.
Gather everything you want before you start talking price. Set the items on the table and ask what the vendor would take for all of them together. This shows you are a serious buyer and lets the vendor do the math once.
Start with a reasonable offer rather than an insulting one. A common approach is to ask for a modest discount first and see how the vendor responds. If the vendor counters, you can meet in the middle, and if the vendor declines, you have lost nothing.
Know your walk-away number before you start. If you have already decided that you would pay a certain total for the pile, you can say yes quickly when the vendor reaches it, and politely leave if the price stays higher.
Round numbers work in your favor. Offering a clean total in cash is simple for both sides and often closes the deal faster than haggling over individual prices.
Be friendly throughout. Vendors remember good customers, and a pleasant bundle negotiation today can turn into a better price the next time you stop by their table.