Preheat oven to 350°F.
Lightly spray a 12-cavity muffin pan with cooking spray and set aside.
Whisk together the flours, flaxmeal, cornstarch, baking soda, baking powder, salt, and cinnamon in a medium bowl.
In as separate bowl, whisk together the non-dairy milk, maple syrup, apple cider vinegar, and vanilla.
Stir the dry into the wet and mix until just combined. No visible white flour should remain, but a few lumps are okay. Do not over mix!
Stir in the shredded zucchini and walnuts, if using, and mix gently to evenly distribute.
Fill each muffin cup about ⅔ of the way full with the batter.
Bake for 22 to 25 minutes until a toothpick inserted in the middle comes out clean.
Let cool in the pan on a wire cooling rack for 10 to 15 minutes before removing them from the pan. The muffins should pop out easily.