Preheat oven to 350 degrees F (175 degrees C). Grease an 8-inch square baking dish. Mix oats, coconut flakes, brown sugar, baking powder, cinnamon, and salt in a bowl. Whisk milk, egg, coconut oil, and vanilla extract together in a separate bowl. Arrange about 2/3 the blueberries into the bottom of the prepared baking dish. Spread the oat mixture over the blueberries. Pour milk mixture over the oats and berries. Sprinkle remaining blueberries evenly over the dish. Bake in preheated oven until golden on top and the oatmeal is set, about 40 minutes. Cool 5 minutes before serving.