Combine butter, lemon juice, pepper flakes, garlic, and salt in pan. Cook over hot side of grill, stirring occasionally, unti butter melts, about 1 1/2 minutes, transfer to cooler side of grill and proceed to grill shrimp, adding parsley just before serving.
Pat shrimp with paper towels. THread shrimp onto 3 skewers, alternating direction of head and tails. Brush both sides of shrimp with oil and season lighly with salt and pepper. Sprnkle one side of each skewer evenly with sugar.
Place shrimp skewers, sugared sides down, on hot side of grill. Grill shrimp, uncovered, until lightly charred, 4-5 minutes. USing tongs, flip and grill until second side is pink and slighly translucent, 1-2 minutes.
Using potholder or oven mitt, carefully lift each skewer from grill; use tongs to slide shrimp off skewers and into sauce. Toss shrimp and sauce to combine and transfer pan to hot side of grill; cook, stirring, until shrimp are opaque and fully cooked, about 30 seconds.