Preheat an oven to 350°F. Sift the sugar 3 times onto a sheet of waxed paper. Sift the flour 3 times onto another sheet of waxed paper. In a medium bowl, combine the sifted sugar and flour with the salt and sift together. Set aside.
In a large, clean, dry bowl, whisk the egg whites for about 3 minutes, or until frothy. Add the cream of tartar and then, using an electric mixer on medium speed, beat until moist, soft peaks form. Be careful not to overbeat to the stiff-peak stage. Beat in the orange zest and almond extract.
Dust a little of the flour mixture on top of the egg whites, then fold it in. Repeat, in small portions, until all the dry mixture is folded in and the batter is light and airy.
Pour the batter into an ungreased 10-inch angel food cake pan with a removable bottom. Bake for 40 to 45 minutes, or until a toothpick inserted into the top comes out clean.
Immediately place the pan upside down on the pan feet, or invert it on the neck of a bottle. Let cool thoroughly at least 1½ to 2 hours before removing from the pan.
Transfer the cake to a cake plate.
To make the frosting: Using an electric mixer on medium high speed, whip the cream until it forms soft peaks. Beat in the sugar until stiff peaks form. Spread the cake top and sides with swirls of whipped cream. Sprinkle generously with coconut flakes, pressing them onto the sides.