Preheat the oven to 350°F (177°C) and line a 9 by 5-inch (23 by 12.75-cm) loaf pan with parchment paper. Leave at least 2 inches (5 cm) of extra parchment on each long side of the pan for easier removal of the loaf.
In a medium-sized mixing bowl, stir together the nondairy milk, sweetener, flax seeds, and vanilla extract. Set aside for 5 minutes, until the flax seeds absorb some of the liquid and thicken, then stir in the pumpkin puree and coconut oil.
In a small bowl, whisk together the soy flour, coconut flour, cinnamon, baking powder, baking soda, and salt.
Stir the dry ingredients into the pumpkin mixture until completely combined and smooth, then scoop the batter into the lined pan and spread evenly. The batter will be too thick to pour, but still loose enough to spread.
Bake for 50 minutes, until a knife inserted in the center of the loaf comes out clean. Let the bread cool in the pan for 5 minutes before removing using the overhanging parchment as handles.
Let cool completely before slicing.