The Flea Market is run by a girl named Claire, who will be visiting your farm once every three days with a list of offers. You can travel freely back and forth across all of your farms to see six new offers for each farm (and can even reload your current farm to see the selection change), but she will only buy one item from you every three days. That is, if you sell an item on your English Countryside farm, you can't suddenly travel to Winter Wonderland and sell something else. Here's a quick run-through of how this works, using a Chicken as an example.
Upon traveling to a farm, you can click on Claire's image in your friends list (she's the first one there now) to see a series of six offers for items currently on that farm. Most of these offers will likely be for coins, but the feature's menus do state "currency" instead of "coins," so there's definitely the possibility that Farm Cash could be offered at some point down the line.
In our example, we can see that a Cornish Chicken can be sold for 225,000 coins. This could be the standard price for the chicken, or it could be a one-time-only price for this particular three day period (that much hasn't been stated exactly). Either way, by parting with this single Cornish Chicken (an animal that can be earned freely through so many other methods), we'd walk away with 225,000 coins free and clear.
Again, Claire will only be available to buy something once every three days, but since you can freely travel across your farms until you find the perfect item to sell (hopefully a duplicate or an item that costs very little to purchase anew in the store), you'll likely never see her talents go to waste. While coins definitely aren't as valuable as Farm Cash, when it comes to massive farm expansions, if you're like me, you'll be happy to score so many coins with such little effort.
Make sure to take advantage of this new feature to clear out some excess animals or items that you no longer need, or just to boost your own wallet every now and again. Who knows, maybe Claire will offer you a bundle of Farm Cash that you can use to spoil yourself with something nice!
Have you tried out the FarmVille Flea Market yet? What did you sell and how many coins did you receive for it? Sound off in the comments.