Can we sell furniture in the Flea Market?

You could use the tarp at your sims home, to have a yard sale. At least I've done that with the street sales table in a Rags to riches challenge. Tried with the one for paintings too, but it was bugged. Never really thought to try the tarp, mostly because my sim couldn't afford buying anything to sell at the time :D

If you decide to try the yard sale out, remember to lock doors. Customers will absolutely make themselves comfortable, eating your food and using whatever they please. :# I ended up with a fence surrounding the house, and locked the gate so nobody could get in.

It would be nice if our sims could see their used furniture that way, but I have not found a way to do so. Maybe someone has created a mod to allow this, I don't know since the game does not allow is to go into buy/build mode to place those items. About the only thing I have been able to do was to sell wall paintings and items that can go on the tables there. But you have to be careful, because if your sim walks away, some other sim will try to step in and take over, and also stealing your sim's stuff. I found this out the hard way.