Preheat oven to 350°F and line two 8-inch or three 6-inch cake pans with parchment paper. Spray pans and parchment with cooking spray.
Whisk together four, baking soda, and salt in a bowl and set aside.
Cream butter on medium-high speed with an electric mixer or stand mixer. Add sugar and mix until fluffy
Add egg whites, vanilla, and butter flavoring; mix well.
Add half of flour mixture and half of milk to sugar mixture. Mix until ingredients are just combined. Add remaining flour mixture and milk; mix until completely combined.
Stir in rainbow sprinkles, stirring as little as possible to prevent the colors from bleeding.
Divide batter among cake pans and bake for 25-28 minutes, or until cakes are lightly golden on top and a toothpick inserted into the center of each layer comes out clean.
Let cakes cool in pans for 5-10 minutes. Transfer to a wire rack to cool completely.