Beat flour, beer, egg, and salt in a bowl with an electric mixer on low until batter is smooth.
Spread coconut flakes in a shallow dish.
Dip shrimp into beer batter, shaking off excess, then press into coconut.
Place shrimp onto a plate while breading the rest; do not stack.
Heat vegetable oil in a skillet over medium-high heat until hot but not smoking, 3 to 4 minutes. Fry about a third of the shrimp in the hot oil until golden brown, 2 to 3 minutes. Allow shrimp to drain on a wire rack set over paper towels. Repeat with remaining shrimp.
