Preheat oven to 350F and grease muffin tin with coconut oil (this is super important, unless you have a silicone doughnut pan).
Stir the ground flaxseed into the water, and let sit for a few minutes.
To the flaxseed mixture, add the canned pumpkin, vanilla, Swerve and coconut oil.
In a separate bowl, mix together the dry ingredients (coconut flour, cinnamon, baking powder, spices).
Stir the dry ingredients into the wet ingredients.
Mix until just combined.
Scoop batter into the wells of the doughnut pan.
Bake for 30 minutes.
You'll be able to tell the doughnuts are done, as they will have separated from the sides of the tin a bit.
Let cool completely before removing from the pan by inverting it onto a cutting board.