Preheat the oven to 350 degrees F. In a small bowl, whisk together the flour, baking powder, soda and salt.
In a large bowl, whisk together the sugar, melted butter and vanilla extract. Quickly whisk in the egg. Fold in the zucchini, pineapple and coconut. Stir in half of the dry ingredients and the chocolate chips. Stir in the milk. Finish with the remaining dry ingredients until just combined, making sure to stir the bottom well.
Heat a 10-inch cast iron skillet over low heat and add the coconut oil. Use a pastry brush to brush the oil all over the bottom and up the sides of the skillet. Turn off the heat and pour the cake batter into the skillet, spreading it evenly.
Bake for 30 to 35 minutes, until the center is set and the edges are golden. Let cool completely before frosting.