Line rimmed baking sheet with triple layer of paper towels, spread beans over towels, and let sit for 15 minutes.

Whisk reserved bean liquid and flour in large bowl until well combined and smooth. Stir in cilantro, hot sauce, if using, cumin, coriander, salt, and pepper until well combined. Process tortilla chips in food processor until finely ground, about 30 seconds. Add black beans and pulse until beans are coarsely ground, about 5 pulses. Transfer bean mixture to bowl with flour mixture and mix until well combined. (Mixture can be refrigerated for up to 24 hours.)

Adjust oven rack to middle position and heat oven to 200 degrees. Divide bean mixture into 6 equal portions. Using your lightly moistened hands, firmly pack each portion into ¾-inch-thick patty. (Patties can be frozen for up to 1 month. Transfer patties to 2 parchment paper–lined rimmed baking sheets and freeze until firm, about 1 hour. Stack patties, separated by parchment paper, wrap in plastic wrap, and place in zipper-lock freezer bag. Thaw completely before cooking.)

Heat 1 tablespoon oil in 10-inch nonstick skillet over medium heat until shimmering. Gently lay 3 patties in skillet and cook until crisp and well browned on first side, about 5 minutes. Gently flip patties, add 1 tablespoon oil, and cook until crisp and well browned on second side, 3 to 5 minutes.

Transfer burgers to wire rack set in rimmed baking sheet and place in oven to keep warm. Wipe out skillet with paper towels and repeat with remaining 2 tablespoons oil and remaining patties. Transfer to buns and top with lettuce, tomato, and avocado. Serve.