In a large mixing bowl, whisk together the sifted flour and sugar until well combined and airy.
Add the melted butter, eggs, vanilla extract, and milk to the dry ingredients. Mix with a spatula or whisk until smooth and no lumps remain; the batter should be slightly thick but pourable.
Divide the batter evenly into several small bowls—one for each color you want for your rainbow. Add a few drops of different food coloring to each bowl, stirring gently until the color is fully incorporated and the batter is vibrant.
Scoop one colored batter into the center of the greased cake pan, then add a different colored scoop directly on top of it, nesting each layer until the pan is filled. The batter will spread out and settle into a pretty rainbow pattern.
Place the cake pan into the preheated air fryer basket. Cook at 320°F (160°C) for about 20 minutes or until the top is golden and a toothpick inserted into the center comes out clean.
Carefully remove the cake from the air fryer and let it cool in the pan for 10 minutes. Then, transfer to a wire rack and cool completely before slicing to reveal the rainbow layers.
Slice the cake with a serrated knife, showing off the colorful interior. Serve as is or with a light frosting or whipped cream if desired.
