Preheat your oven to 375 degrees F. Line a baking sheet with parchment paper.
Sprinkle flour on a work surface. Roll out pie dough to form a 10-inch circle and place on baking sheet. Overlap and alternate the different tomatoes and mozzarella slices in the center of the dough, leaving a 3-inch border. Scatter the basil leaves on top. Sprinkle with salt and pepper and red pepper flakes. Fold the uncovered edges of the dough inward over the filling to create a pleated crust. Brush edges and top of pie with olive oil.
Place in the oven and bake for 35 minutes. Remove from the oven to a cutting board. Slice and serve.