Preheat oven to 180°C.
In a medium-sized bowl, whisk together the ground flaxseeds and water. Set aside for 5 minutes to thicken.
Add the applesauce, coconut sugar and vanilla to the flaxseed mixture. Whisk until uniform.
In another bowl, whisk together the oat flour, brown rice flour, tapioca starch, baking powder, baking soda, cinnamon and nutmeg. Whisk until uniform and lump-free.
Pour the wet ingredients into the dry. Stir until evenly mixed.
Pour the batter into the prepared baking pan and bake for 45-50 minutes, until browned on top and a toothpick comes out clean.
Allow the cake to cool completely before serving.