Heat oven to 375°F and arrange a rack in the middle. Grease 12 muffin cups or line them with paper liners.
Combine flour, oats, sugar, whole wheat flour, baking powder, salt, and nutmeg in a medium bowl.
Whisk together milk, coconut oil, and egg in a large bowl. Add dry ingredients all at once to the wet ingredients and stir until just moistened. Fold in coconut.
Evenly divide batter between the muffin cups and bake until firm to the touch and a toothpick inserted in the center comes out clean, about 20 minutes. Let cool in the pan for about 5 minutes, then transfer to a wire rack to cool.
These muffins are incredible warm, but keep well in an airtight container at room temperature for up to 4 days.