Preheat the oven to 375°F. Combine the cake flour with 5/8 cup of the sugar and the salt, then sift this mixture together five times into a bowl. This aerating process removes lumps and creates the foundation for a delicate crumb. Set aside and verify that all mixing bowls and beaters are completely free of grease.

Place the room-temperature egg whites in a large mixing bowl and beat at medium speed until frothy. Add the cream of tartar and continue beating until the mixture becomes foamy. Mix in the vanilla extract and almond extract, then begin adding the remaining 5/8 cup of sugar one tablespoon at a time while maintaining medium speed. This gradual incorporation builds fine, stable air bubbles.

Turn the mixer speed up to medium-high and continue beating until the egg whites form stiff peaks that stand straight when the beaters are lifted. Divide the sifted flour mixture into four portions and gently fold each portion into the meringue using a spatula, making 15 to 20 careful strokes after each addition. Stop folding when a few flour streaks remain visible rather than overmixing.

Transfer the batter into an ungreased 10-inch angel food cake pan, allowing it to cling to the sides for proper rise. Gently smooth the surface with a spatula, then run a thin knife through the batter in circular motions several times to eliminate large air pockets. Bake for 15 to 20 minutes until the top turns golden and bounces back when gently pressed.

Immediately upon removing the cake from the oven, flip it upside down onto a cooling rack or position the center tube over a bottle neck to allow air circulation underneath. This inverted cooling prevents the delicate structure from collapsing. Allow the cake to cool completely for at least 1 hour. Once cooled, release the cake by running a thin knife around both the outer edge and center tube, then turn it out onto a serving plate.

In a chilled bowl, beat the heavy cream with the powdered sugar and vanilla extract until stiff peaks form. Cover the top and sides of the cooled cake with most of the whipped cream. Create a flag pattern by arranging the sliced strawberries and blueberries in alternating stripes and sections. Use the remaining whipped cream to pipe or dollop decorative accents between the berry rows. Refrigerate the assembled cake for 15 to 30 minutes before serving to set the cream and keep the berries fresh.