I highly recommend the Brooklyn Flea on weekends from April through Thanksgiving. There are two locations. On Saturday you can hit the one in Ft. Greene. I enjoyed exploring this Saturday market at 176 Lafayette Ave. On Sunday the vendors move to Williamsburg. There is also a winter market during the off season. Make sure to check out the website for all market details and vendors.
There is also the Brooklyn Flea Food Market or Smorgasburg on Saturdays, near the East River in Williamsburg, between N. 6th and N. 7th. Here you can find many local restaurants and food trucks offering every imaginable ethnic food. It is a festive atmosphere so head over for lunch. On Sundays the market moves to the Brooklyn Bridge Park