Preheat oven to 400˚F (200˚C). Grease two sheets of parchment paper (about 12 x 16 inches/30.5 x 40.5 centimeters each) with butter or margarine.
In a large bowl, mix together the flour, coconut flakes, sugar, baking powder, and salt.
Slowly mix in the coconut milk to form a dense dough with no crumbly pieces remaining. You may not need the full 1 cup (240 milliliters) coconut milk or you may need slightly more.
Divide the dough into two equal pieces.
Place one piece on a greased sheet of parchment and form into a rectangle about 1 inch (2.5 centimeters) thick.
Fold up the parchment over the dough to cover, starting with opposite ends, then the other opposite ends. Place the parchment-wrapped dough on a rimmed baking sheet, folded side down.
Place the other piece of dough on the other sheet of greased parchment, also 1 inch (2.5 centimeters) thick. Fold the edges in to cover and place on the rimmed baking sheet next to the other wrapped dough.
Bake in the preheated oven until the bread is lightly puffed and golden around the edges, 30-40 minutes.
Remove from the oven, unwrap, and allow to cool to room temperature.