Preheat oven to 375 degrees F (190 degrees C). Grease 12 muffin cups or line with paper muffin liners.
Mix all-purpose flour, whole wheat flour, flaxseed, baking soda, and salt together in a small bowl.
Beat orange juice, egg whites, almond milk, brown sugar, and honey together in a large bowl until smooth. Stir flour mixture into the orange juice mixture just until the dry ingredients are moistened completely. Fold walnuts through the batter. Spoon batter into the prepared muffin cups.
Bake in preheated oven until lightly browned and a toothpick inserted into the center of a muffin comes out clean, 15 to 20 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.