Preheat the oven to 350°F. Wrap stack of tortillas in aluminum foil, set in oven, and warm 5 to 7 minutes.
Meanwhile, heat olive oil in large heavy skillet over moderately high heat until ripples appear on skillet's bottom, about 1½ to 2 minutes. Add onion and sauté, stirring often, until limp, about 3 minutes. Add garlic, cumin, black pepper, red pepper flakes, red pepper sauce, and black beans. Cook and stir just until heated through, about 2 minutes. Set off heat but keep warm.
Heat mango, brown sugar, and lemon juice in small nonreactive skillet over moderately high heat just until mango softens and juices appear, about 1 minute.
To assemble burritos, place ⅓ cup black bean mixture down the center of each tortilla, then sprinkle with cheese, dividing total amount evenly. Roll tortillas up and place seam sides down on six dinner plates.
Dividing all amounts equally, top tortillas with yogurt, then mango mixture, then diced tomatoes and chopped cilantro. Serve immediately.
Notes
If you're going to assemble them individually, you may wish to microwave the tortillas. Place one tortilla on a plate, then add bean mixture & sprinkle cheese on top. Microwave until hot and then continue with assembling.