Preheat oven to 350°F. Grease an 8-inch round cake pan. Line bottom with parchment paper. Set aside 1 tablespoon of powdered sugar.
Whisk the almond meal, coconut flour and remaining powdered sugar in a large bowl. Set aside.
Use a mixer to beat egg whites on medium speed until frothy (about 1 minute), mix in cream of tartar, salt and 1 tablespoon of the sugar, then beat at high speed until the egg whites hold stiff peaks, about 2 minutes. Set aside and proceed immediately to the next step (the whites will fall if left for more than a few minutes).
In a separate bowl, beat the egg yolks at medium speed until frothy. Add the almond and vanilla extracts, then beat on high until pale yellow and smooth. Gradually add the flour mixture, a little at a time, folding in the last of it by hand. Fold in 1 cup of the beaten egg whites to lighten the batter, then gently fold in the remaining whites.
Spread the batter in the prepared pan, smoothing the top. Bake 20 minutes, or until the cake is puffy and golden and a knife inserted in the center comes out clean.
Set pan aside to cool completely. It will deflate somewhat. Sprinkle with coconut flakes and slivered almonds.