Preheat oven to 375 degrees F (190 degrees C). Grease a 9x5-inch loaf pan with 1 teaspoon coconut oil.

Place 1/4 cup coconut oil in a microwave-safe bowl; heat in microwave until melted, about 30 seconds.

Mix flour, ground flaxseeds, ginger, baking soda, cinnamon, allspice, and sea salt in a large bowl.

Combine brown sugar, melted coconut oil, and egg in a separate large bowl; add squash puree, coconut milk, molasses, and vanilla extract and mix well. Stir flour mixture into squash mixture until batter is smooth. Pour batter into the prepared loaf pan and smooth the top.

Bake in the preheated oven until a toothpick inserted in the center comes out clean, 45 to 55 minutes. Cool for 5 minutes before turning cake onto a wire rack to cool completely.