Preheat the oven to 350 degrees Fahrenheit.
Add the coconut flour, ground flaxseed, and baking soda to a mixing bowl, then mix well.
Add the pumpkin purée, almond butter, maple syrup, apple cider vinegar, pumpkin pie spice, salt, and vanilla extract to a second mixing bowl, then use a whisk to mix well.
Add the dry ingredients to the wet ingredients, then use a spoon to stir to combine (the batter will be very thick).
Spoon the batter into a 9-inch loaf pan lined with parchment paper.
Wet a spoon with cold water, then use the back of the spoon to smooth the batter into an even layer.
Bake for 50 minutes or until a toothpick inserted into the middle of the bread comes out looking clean.
Let the pumpkin bread cool to room temperature before removing from the pan and serving.