Whisk together mayonnaise, sweet chili sauce, sriracha, honey, and garlic powder in a small bowl until smooth. Taste and adjust sriracha to your heat preference. Set aside.
Pat shrimp completely dry with paper towels. Toss with smoked paprika, garlic powder, onion powder, salt, and black pepper until evenly coated.
Heat oil in a cast iron skillet over medium-high heat until shimmering. Sear shrimp in a single layer, 2 minutes per side, until pink, cooked through, and slightly golden at the edges. Remove from heat immediately.
Warm tortillas in the microwave for 20 seconds or in a dry skillet until pliable.
Layer fillings down the center of each tortilla: rice first, then black beans, shrimp, cheese, green onions, and a generous drizzle of Bang Bang sauce. Leave 2 inches on each side.
Fold in the sides of the tortilla, then roll tightly from the bottom up, keeping the burrito compact.
Place the Bang Bang Burrito seam-side down in a dry skillet over medium heat. Sear 1-2 minutes per side until the exterior is golden and crispy.
Slice diagonally, drizzle with additional Bang Bang sauce, and garnish with green onions and red pepper flakes. Serve immediately.