Preheat the oven to 350°F. Grease two 9-inch round cake pans, line the bottoms with parchment paper, then grease the parchment. Dust lightly with gluten free flour and tap out the excess.
In a large bowl, whisk together the gluten free flour, granulated sugar, baking powder, and salt. Add the softened butter and beat with an electric mixer on medium speed for about 2 minutes until the mixture looks like coarse, sandy crumbs.
In a separate bowl, whisk together the egg whites, milk, vanilla extract, and almond extract. Pour half of this wet mixture into the flour-butter crumbs and beat on medium speed for about 1 minute until smooth and fluffy.
Add the remaining wet mixture and beat for 30 seconds more until just combined. Gently fold in the rainbow sprinkles with a spatula, being careful not to crush them or overmix.
Divide the batter evenly between the two prepared pans and smooth the tops. Bake for 28 to 32 minutes, until a toothpick inserted in the center comes out clean and the edges just begin to pull away from the sides.
Let the cakes cool in the pans for 10 minutes, then run a spatula around the edges and turn them out onto a wire rack. Peel off the parchment and let them cool completely before frosting.
To make the frosting, beat the softened butter with an electric mixer on medium-high speed for 3 minutes until pale and creamy. Add the powdered sugar one cup at a time, beating on low speed after each addition until incorporated.
Add the heavy cream, vanilla extract, and salt, then beat on medium-high for 2 to 3 minutes until the frosting is light, fluffy, and smooth.
Place one cake layer on a serving plate and spread about 1 cup of frosting evenly on top. Set the second cake layer on top, then frost the top and sides with the remaining frosting using an offset spatula.
Press gluten free rainbow sprinkles generously onto the sides of the cake and scatter more on top. Let the cake rest for 15 minutes before slicing so the frosting sets. Store covered at room temperature for up to 2 days.