Preheat oven to 350°. Line two 8-inch cake pans with parchment paper and grease with cooking spray.
Make cake: In bottom of a small bowl, stir together about 5 drops of a gel food coloring and 3⁄4 teaspoon water. Add1⁄3 cup coconut and stir until coconut flakes absorb color. Repeat in separate bowls with remaining coconut flakes and colors. Set aside.
In a medium bowl, whisk together almond flour, coconut flour, baking powder, baking soda, and salt.
In a large bowl, beat butter and sweetener until light and fluffy, about 2 minutes. Add eggs, egg whites, and vanilla. Beat until well combined and foamy, about 1 minute. Add dry ingredients to wet and beat to combine. Add almond milk and vinegar and beat until combined.
Add all but a spoonful of each color of coconut flakes; fold to combine. Divide batter between baking pans and smooth top. Bake until toothpick inserted into center of cakes comes out clean, 50 minutes. Let cool completely.
Make frosting: In a large bowl, beat butter, cream cheese, sweetener, cocoa powder, and salt until light and fluffy, about 2 minutes. In a microwave-safe bowl, microwave chocolate chips until just melted. Pour melted chocolate into butter mixture and beat until well combined.
Using a serrated knife, remove domed tops of cakes to even. Place one cake on a platter or cake stand. Spread 1 1⁄2 cups frosting onto top of cake layer. Top with remaining cake; frost top and sides with remaining frosting. Sprinkle top of cake with reserved colored coconut.