Flea Market at Rhinebeck31 Oct, 2016 in New York by mfgadmin Flea Market at Rhinebeck Held 2 weekends per year – in April and September. Call for dates and times. Located at the Duchess County Fairgrounds. Open: Saturdays and Sundays. Location: 6550 Springbrook, Rhinebeck, NY 12572 Phone: 845-876-4001