Coat a 13 x 9-inch baking pan with cooking spray; dust with flour.
Combine cake mix and next 5 ingredients (cake mix through egg); beat at low speed of a mixer for 30 seconds. Beat at medium speed for 2 minutes. Pour half of batter into prepared pan. Sprinkle with flaked coconut and brown sugar; top with remaining batter. Bake at 350° for 30 minutes or until a wooden pick inserted in center comes out clean. Cool the cake completely in pan. Spread the Coconut-Cream Cheese Frosting over top of cake.