Preheat oven to 400° F. Spray a muffin tin with cooking spray or line with paper liners.
Place oats in a food processor and pulse a few times until they resemble a coarse meal. Transfer to a large bowl.
Add the next 7 ingredients (flours through salt) to the oats and stir well to combine. Make a well in the center of the mixture.
Combine buttermilk, oil, 2 teaspoons lemon zest, and eggs in a small bowl; whisk well.
Add wet ingredients to the well in the flour mixture, then stir together just until moist.
Toss berries with 2 tablespoons flour, and gently fold them into the batter.
Spoon batter into muffin cups and bake for 20 minutes or until muffins spring back when touched lightly in the center.
Remove from pans immediately and place on a wire rack to cool before serving.