Preheat oven to 350 degrees F (175 degrees C). Lightly grease an 8x10-inch baking pan.
Mix oats, brown sugar, flax seed meal, flour, baking powder, cinnamon, and salt together in a bowl. Mix banana, rice milk, egg, and vanilla extract together in a separate bowl. Pour banana mixture into flour mixture; stir to combine. Pour batter into the prepared baking pan.
Bake brownies in the preheated oven until a toothpick inserted in the center comes out clean, about 20 minutes. Cover pan with a towel to hold in moisture and cool brownies for at least 5 minutes before serving.