Prepare crust: On a lightly floured board, stack 2 pastry disks (1 pkg.; enough for a 2-crust pie) or use 1 batch Best Basic Pie Crust Dough and roll into a 16- by 21-in. rectangle, applying a little more pressure at edges to even out corners. Fit pastry into a well-buttered and floured 13- by 18-in. rimmed baking pan (aka half-sheet pan), filling corners; roll edges under on top of rim and crimp slightly so pastry sticks to pan rim. Chill, covered with plastic wrap.
Reflour board, stack remaining pastry disks (or use remaining batch Best Basic Pie Crust Dough), and roll into a 12- by 17-in. rectangle. With a small star-shaped cookie-cutter, cut out 8 or 9 stars for the upper left quadrant of flag pie. For stripes portion of flag, use a ruler and a large knife to cut 7 or 8 (1/2-in.-wide) strips: 3 of them 9 1/2 in. long and the rest 15 1/2 in. long. Sprinkle a large flat baking sheet with flour, set pastry cutouts on baking sheet, and chill, covered with plastic wrap.
Meanwhile, make filling: Put blueberries in a small bowl and toss with 3 tbsp. sugar, 2 tsp. cornstarch, and 2 tsp. lemon juice. In a large bowl, combine strawberries and raspberries and gently toss with remaining sugar, cornstarch, and lemon juice.
Preheat oven to 375° with a rack in bottom position. Pour blueberry filling into top left quadrant of crust, for star area (about 5 by 6 in.). Pour strawberry-raspberry filling into rest of crust. Arrange cutout pastry stars over blueberries and stripes over strawberry-raspberry filling.
With a fork, blend egg and cream together in a small bowl. Brush stars and stripes with egg wash and sprinkle with turbinado sugar.
Bake pie on bottom rack until pastry is golden brown and filling is bubbling, 60 to 70 minutes; if the fruit is getting too dark, cover loosely with foil (check halfway through).
Let cool on a rack for at least 2 hours before serving.