Preheat the oven to 400 degrees F (200 degrees C). Grease a 9x13-inch baking pan.
Beat together sweetener, butter, water, and flaxseed meal using an electric mixer in a mixing bowl until creamy. Pour in milk and eggs; mix well. Add brown rice flour, almond meal, cornmeal, quinoa flour, polenta, baking powder, salt, and vanilla extract. Mix until well combined and smooth.
Pour batter into the prepared baking pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 22 to 27 minutes.