Preheat the oven to 350°F. Prepare three 6-inch or two 8-inch cake pans by spraying the sides with baking spray (Baker's Joy is my favorite) and lining the bottom with parchment paper. Alternatively, you can grease and lightly flour the pans.
In a medium bowl, add the sifted cake flour, baking powder, baking soda, and salt. Whisk to combine and set aside.
In the bowl of your stand mixer fitted with the paddle attachment (or with a large bowl and handheld mixer), cream the butter and sugar until light and fluffy, about 4 minutes, scraping down the bowl and paddle once in between. Turn the mixer to low speed and add the eggs one at a time, mixing for about 10-15 seconds after each addition. Add the vanilla and sour cream, then mix for one minute on high speed. Scrape down the bowl and paddle.
Turn the mixer off and add the dry ingredients all at once, then mix on low speed. When the ingredients just begin to incorporate, add the milk slowly and mix until just incorporated, about 30 seconds. Scrape down the sides and bottom of the bowl and give it a few stirs by hand to make sure there are no large lumps.
In a small bowl, coat the rainbow sprinkles with 1 teaspoon of flour (cake flour or all purpose flour). Then, gently fold the flour-coated rainbow sprinkles into the cake batter with a silicone spatula. The batter will be slightly thick.
Pour batter into prepared cake pans and bake for 30-35 minutes. They're done when they spring back to the touch and a toothpick inserted into the middle comes out clean. Let the cakes cool in the pan for five minutes before turning them out onto a wire rack for an additional few hours of cooling. Make sure they're entirely room temperature before filling and frosting with vanilla buttercream (or frosting of your choice).