Border Flea MarketOctober 29, 2016 in Texas by robl Border Flea Market Hundreds of Vendors. Held year around except Thanksgiving Day and Christmas Day. Indoor market. Open: Thurs: 10am – 5pm; Fri – Sun: 10am – 7pm. Location: 1045 Mexico Blvd, Brownsville, TX 78520 Phone: 956-541-6900