Combine flour, cornmeal, baking powder, baking soda, and salt in a mixing bowl, stir with a fork, and set aside. In a food processor or blender, process brown sugar, corn, and rice milk/vinegar mixture until combined, about 5 seconds. Add eggs and oil and process another 5-10 seconds. Use a rubber spatula to fold the wet ingredients into the dry ones. Barely mix, just make sure the dry ingredients are moistened. Pour batter into prepared baking dish, smooth surface. Bake until the top is golden brown and a knife blade (not a toothpick!) inserted in center comes out clean, about 35-40 minutes. Cool on rack for 10 minutes. Invert on a wire rack and then onto a serving plate. Wait about 10-15 minutes to cut.