Make the cake: Position a rack in the center of the oven and preheat to 325ºF. Butter the bottom only of a 9- by 12-inch or 9- by 13-inch cake pan. The cake batter will crawl up the ungreased sides of the pan, making for a taller, lighter cake that will better absorb the milk mixture.
In a very large bowl, whisk together 1/4 cup water wiht the oil, egg yolks and vanilla, then whisk in the 1⁄2 cup sugar. Place a strainer over the bowl and sift the millet, sweet rice, and oat flours with the baking powder and salt directly into the yolk mixture, adding back any bits left behind in the strainer. Whisk until very smooth and the consistency of pancake batter.
In the clean, dry bowl of a stand mixer fitted with the whip attachment, whip the egg whites with the cream of tartar on medium-high speed until soft peaks form. Slowly add the remaining 2 tablespoons sugar and whip until the whites are glossy and just hold a firm peak when lifted from the bowl, 1 to 3 more minutes.
While the cake is cooling, make the milk mixture: Combine the coconut milk, sweetened condensed coconut milk, vanilla, and salt in a medium saucepan. Warm over medium heat, stirring until combined and warm to the touch. Keep warm; this will help the mixture absorb into the cake.
To serve: Top the cake with the whipped coconut cream and berries. Cut into squares or wedges and enjoy.