Preheat the oven to 350 degrees and line a baking sheet with parchment paper. Place 1 1/4 cup of the rolled oats in the food processor or a blender and process until it is a fine flour.
In a small bowl, add the flaxseed and water and let thicken for 3-5 minutes. Set aside.
In a large bowl, add the oat flour, 1 cup of whole rolled oats, baking powder, baking soda, and cinnamon, and stir. Stir in the quinoa and shredded carrots. Stir until combined.
In a large bowl, combine the peanut butter, melted coconut oil, and maple syrup. Stir until combined. Pour in the flaxseed mixture and stir. Add the wet ingredients to the dry ingredients and stir until combined. Fold in the walnuts and coconut flakes.
Scoop approximately 2 tablespoons of batter for each cookie and place it on the baking sheet. Bake for 15 to 18 minutes, or until lightly browned. Cool on the pan for 3-5 minutes and then transfer to a wire rack to finish cooling.