Place the mangoes, brown sugar, Worcestershire sauce, tamarind paste, oil, red pepper flakes, and garlic in a blender. Puree until smooth.
Place the chicken in a large bowl and season with salt and pepper. Add just enough sauce to coat the wings (about 1/2 cup, reserve the rest for serving) and toss to coat. Cover the wings with plastic wrap and refrigerate for at least 30 minutes or up to 1 hour.
Preheat the oven to 350 degrees F. Line a baking pan with aluminum foil and lightly coat with nonstick cooking spray. Lift the chicken wings out of the sauce letting the excess marinade drip back into the bowl. Place the wings on the prepared baking pan and bake for 30 minutes until cooked through. Preheat the broiler and adjust the rack so it's 6 inches from the heating element. Transfer the wings to the broiler and broil for another 3 minutes until the skin is crispy.
While the wings bake, place the reserved sauce in a small saucepan and bring to a boil. Reduce the heat to medium-low and simmer until syrupy, 5 to 10 minutes. Put the chicken on a platter and garnish with chopped scallions. Serve with the remaining mango-tamarind sauce on the side for dipping.