Coconut Fry Bread (aka Coconut Bake in Trinidad and Tobago)

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2 pounds all-purpose flour

2 tablespoons granulated sugar 

1 tablespoon baking powder 

2 teaspoons salt 

1 1/2 tablespoons shortening 

1 tablespoon butter, at room temperature 

1 1/4 cups water 

1 cup coconut milk 

1/2 cup unsweetened coconut flakes 

Vegetable oil, for frying