Preheat the oven to 350ºF (180ºC). Line the bottoms of three 6-inch cake pans with parchment paper. Grease and flour the insides.
In a large bowl, whisk together the flour, baking powder and salt until well blended.
In a large bowl, beat the butter, sugar and oil and coconut extract together with an electric mixer at medium speed, until pale and fluffy, about 2-3 minutes. Gradually beat in egg whites until the mixture is smooth and creamy, stopping to scrape the sides of the bowl as needed.
On low speed, beat in flour mixture in 3 additions, alternating with the coconut milk after each addition.
Pour batter into the prepared pans, evenly distributing batter among the pans. Bake for 28-32 minutes, until a toothpick inserted into the center of the cakes comes out clean.
Cool the cakes for 10 minutes. Remove the cakes from pans and transfer them to a cooling rack.