Preheat a medium skillet or griddle over medium heat. Lightly grease with cooking spray.
In a blender or food processor, add oats. Blend until a fine flour forms.
To a large bowl, add oat flour, all-purpose flour, flax, baking powder, baking soda, cinnamon, and salt. Stir to mix. Add milk, oil, and vanilla. Whisk to combine; do not overmix.
Add peaches; gently fold into batter. Let the batter sit for 5 minutes.
Pour 1/4 cup of batter in the pan to form each pancake. Cook on one side until bubbles begin to form, about 3-5 minutes. Flip and cook about 3-5 more minutes. Repeat until batter is used up.