In a mixing bowl, whisk together the flour and sugar until evenly combined. Add the melted butter, eggs, milk, and vanilla extract, and whisk until the batter is smooth and free of lumps.
Gently fold in the rainbow sprinkles, making sure they are evenly distributed throughout the batter. The batter will be slightly thick but pourable.
Grease your mini loaf or cake pan with a little butter or non-stick spray to prevent sticking. Pour the batter into the prepared pan, smoothing the top with a spatula.
Place the pan inside your air fryer basket, ensuring it fits comfortably. Set the air fryer to 330°F (165°C) and cook for about 20 minutes, or until the top is golden and a toothpick inserted in the center comes out clean.
Once cooking is complete, carefully remove the pan from the air fryer. Let the cake cool in the pan for a few minutes until it sets slightly, then transfer to a wire rack or plate.
Slice into the tender, colorful cake and enjoy immediately, reveling in the soft crumb and cheerful sprinkles throughout.