Preheat oven to 400 degrees F (200 degrees C). Butter a muffin tin.
Combine baking mix, milk, sugar, egg, and vegetable oil in a bowl. Mix well. Fold in 3/4 cup coconut flakes and 1/4 cup chocolate chips. Fill prepared tin with batter; sprinkle remaining coconut flakes on top.
Bake cupcakes in the preheated oven until a toothpick inserted into the center comes out clean, 15 to 18 minutes. Let cool, about 10 minutes.
Melt the remaining 1/2 cup chocolate chips in a microwave-safe glass or ceramic bowl in 15-second intervals, stirring after each melting, about 1 minute. Drizzle melted chocolate over cooled cupcakes.