Make the crust: Roll out half the dough and fit it into a greased 10-inch pie plate and crimp the edges. Place the other rolled-out crust on a baking sheet. Freeze both crusts for 30 minutes.
Remove the crust on the baking sheet from the freezer. Using a pizza cutter and a ruler, measure out 1-inch strips; cut three full-length, i.e., 10- or 11-inch strips and two half-length strips. Use the remainder of the dough to cut out the stars using a cookie cutter. Place stars and stripes back on to the baking sheet and freeze until ready to use
Make the fillings: In a large bowl, combine the strawberries, sugar, cornstarch, salt, lemon juice and vanilla. In a separate smaller bowl, combine the blueberries, sugar, cornstarch, salt, lemon juice and vanilla.
Assemble the pie: To keep your blueberry and strawberry fillings separate, make a barrier: Cut a strip of aluminum foil about 2 inches wide and fold it in half lengthwise so you have an inch-wide strip. Then crease it in half widthwise to create an “L” shape.
Remove the crimped crust from the freezer. Place the L-shaped foil piece in the top left corner of the pie crust, creating a compartment that is a quarter of the whole pie in size. Sprinkle the ½ teaspoon each of flour and sugar over the crust base; this will help prevent a soggy bottom.
Pour the blueberry filling into the smaller section and the strawberry filling into the larger section. Remove the foil and adjust the berries, if some rolled out of place.
Remove the dough stripes and stars from the freezer. Place the stars and stripes on the berry fillings to resemble a flag, being sure to press the ends of the stripes into the edge of the bottom crust.
Brush the entire crust with egg wash, making sure not to pull the berries’ sugary syrup onto the crust, as it will burn. Sprinkle finishing sugar over the whole thing for a sparkly finish. Freeze entire pie for 30 minutes before baking.
Bake the pie: Preheat the oven to 375 degrees. Place the pie on a baking sheet and then on the center rack of the oven. Bake for 1 hour to 1 hour and 15 minutes, rotating the pie 90 degrees every 15 minutes. The pie is done when it is golden brown and sparkling from sea to shining sea. Let the pie cool for at least 3 hours, then enjoy à la mode!