Preheat oven to 400º F. Prepare a parchment lined rimmed baking sheet and set aside.
Dry the shrimp with paper towels until they are completely dry. Arrange them on additional paper towels. Stir together salt, pepper, paprika, chili powder, and red pepper flakes and sprinkle on top of shrimp.
Stir together panko, flour and coconut in a shallow dish.
Dip shrimp into egg whites and then into the panko mixture, pressing the coating onto the shrimp gently to make sure it adheres. Place coated shrimp onto the rimmed baking sheet as you prepare the other shrimp.
Spray coated shrimp lightly with cooking spray and then place in the oven to bake until shrimp turn light pink and the panko and coconut are lightly toasted, about 10 minutes.