Toss together red onion, vinegar, Adobo seasoning and brown sugar. Let stand for 15 minutes; drain well.
Meanwhile, toss together chicken and chipotles until well coated; set aside. Pour enough oil into skillet to come 1/2 inch up side; heat over medium heat. Working in batches, fry tortillas for 2 to 3 minutes or until golden brown and crisp; transfer to paper towel-lined tray.
Top tostadas with refried beans, cabbage, chicken mixture, pickled red onions and avocado. Serve with Salsa Verde, Salsa Taquera and lime wedges.