Preheat the oven to 350°F.
Lightly oil and line the bottoms of a couple 9-inch round baking pans with parchment paper.
Stir the flour, sugar, baking powder, baking soda, and salt together in a large mixing bowl.
In a smaller bowl or liquid measuring cup, stir together the milk, coconut oil, vinegar, vanilla extract, and coconut extract.
Beat the ingredients together using an electric mixer at high speed, just until combined, about 1 minute.
Fold in the coconut.
Divide the batter among the prepared cake pans.
Bake the cake layers for about 25 minutes, until the tops are golden and a toothpick inserted into the center of one comes out clean.
Transfer the cake layers to a cooling rack and let them cool completely.