Heat oven to 350°F (325°F for dark or nonstick pan). Spray bottom only of 13x9-inch pan with baking spray with flour. Reserve 1/3 cup coconut milk for frosting.
In large bowl, beat cake mix, remaining coconut milk (1 1/3 cups), the water and egg whites with electric mixer on low speed 30 seconds, then on medium speed 2 minutes, scraping bowl occasionally. Stir in 1/2 cup of the coconut until well combined. Pour into pan.
Bake as directed on box for 13x9-inch pan. Cool completely; about 1 hour.
Meanwhile, in 2-quart bowl, microwave vanilla baking chips uncovered on High about 30 seconds or until melted. Stir; if chips are not completely melted, microwave 15 seconds longer, then stir until all chips are melted. Stir in powdered sugar, butter, reserved 1/3 cup coconut milk and the vanilla. Cover; refrigerate 30 to 60 minutes. (If frosting becomes too firm to spread, microwave uncovered on High 10 to 15 seconds to soften; stir until smooth.)
Spread frosting over cake. Immediately sprinkle top with 1/4 cup coconut. Store loosely covered.