Preheat oven to 350 degrees F. Grease and flour two 8" x 4" loaf pans.
Spread walnuts in a single layer on an ungreased baking sheet. Toast in the preheated oven for 8 to 10 minutes or until lightly browned. Set aside to cool.
In a large bowl, stir together the flour, brown sugar, white sugar, baking soda, salt, nutmeg, and cinnamon. Add the pumpkin puree, oil, and coconut milk, and mix until all of the flour is absorbed. Fold in the flaked coconut and toasted walnuts. Divide the batter evenly between the prepared pans.
Bake for 1 hour and 15 minutes in the preheated oven or until a toothpick inserted in the center comes out clean. Remove from oven, and cover loaves tightly with foil. Allow to steam for 10 minutes. Remove foil, and turn out onto a cooling rack. Tent loosely with the foil, and allow to cool completely.