Preheat the oven to 350°F.
Oil the inside of 3 (9-inch) round cake pans, then line the bottoms of the pans with parchment paper. Oil the parchment paper, then flour the insides of the pans.
Whisk the flour, cornstarch, 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 milk, vinegar, vanilla extract, coconut extract, and almond extract.
Pour the milk mixture into the bowl with the flour mixture, then beat at high speed with an electric mixer until fully combined, about 1 minute.
Fold the coconut into the batter.
Divide the batter evenly among the prepared cake pans.
Bake the cake layers for about 15 to 17 minutes, until the tops are golden and a toothpick inserted into the center comes out clean.
Transfer the cake layers to a cooling rack and let them cool completely.