Preheat your oven to 350 degrees. Grease a 9x9 square pan with coconut oil.
Melt 1/4 cup of coconut oil and let it cool while preparing your other ingredients.
Beat eggs, coconut milk, xylitol, stevia, and key lime juice until well combined.
Mix baking powder, salt, lime zest, coconut flour, and coconut flakes together in a separate bowl.
Beat the two mixtures together and then add the coconut oil.
Pour the cake batter in the 9x9 pan and bake at 350 degrees for 35 - 40 minutes.
Allow the cake to thoroughly cool before making icing.