Preheat oven to 350°F. Coat three 6×2-inch round cake pans with flour-based baking spray.
Sift together the flour, baking powder and salt. In a separate bowl, whisk together the egg whites and milk.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter until creamy. Add sugar and beat until fluffy. Scrape down the bowl as needed.
Add flour mixture alternately with the egg white/milk mixture. Begin and end with the flour mixture. Beat until smooth on medium-low speed after each addition. Divide batter evenly into three bowls. This will be about 1 2/3 cups of batter per bowl.
Divide boiling water into three separate small bowls (1/4 cup each bowl). Stir the cherry, raspberry, and unflavored gelatin in each of the three bowls (gelatin may not totally dissolve – this is okay). Add the lime oil to the bowl with the unflavored gelatin and stir well.
Stir the cherry gelatin into one bowl of cake batter and add the red food color. Fold until well combined. Stir the berry blue gelatin into another bowl of batter and add the sky blue food color. Fold until well combined. Add the lime flavored gelatin to the last bowl of batter and fold until well combined. Pour each batter into a prepared 6-inch pan about 3/4 full. Bake for 35-40 minutes, or until cakes are firm and a toothpick tester inserted near the center comes out clean or with a few moist crumbs attached. Remove cakes from pans and allow to cool completely.
Level cakes if needed. The blue and red layers will not crown much. The white layer may puff a little taller than the other two, so it will need to be leveled.
For the buttercream
In the bowl of an electric mixer fitted with the whip attachment, beat the butter until creamy. Add the confectioners’ sugar and salt. Mix until thick and crumbly. Add milk or cream a little at a time until the mixture is thin and begins to whip into fluffy frosting. You may need to use more or less milk depending on the cornstarch content in your confectioners’ sugar. Beat in the vanilla extract. Beat frosting on high for 3-4 minutes, or until the frosting loses its yellow color and turns almost white.
Spread a small amount of frosting on the blue cake layer, and place it on a cake board or cake stand. Top the blue layer with the white layer. Spread a small amount of frosting on the white layer and top with the red layer. Frost entire cake with a thin coat of buttercream (crumb coat). Refrigerate until firm.
Divide the remaining buttercream into three portions. Tint two portions with the red food color and blue food color. Leave one portion without color. Transfer each color of buttercream to disposable piping bags with 1/2-inch hole cut in the ends. Pipe three fat lines of blue buttercream on the bottom third of the cake. Pipe three fat lines of white buttercream just above the blue so that 2/3 of the cake is now covered. Pipe the remaining 1/3 side of the cake with the red buttercream, and then pipe it onto the top of the cake. Use a cake smoother or bench scraper to smooth the sides of the cake, removing some of the frosting so that the colors meld together. Smooth the top of the cake with an offset spatula.
Pipe more white frosting on top of the cake and garnish with assorted sprinkles. Store cake under plastic wrap at room temperature.