Heat oil in a small frying pan over low heat until hot, about 1 minute. Add chile flakes and remove from heat. Let cool to room temperature. Strain through a fine mesh strainer if desired, then transfer to a container and cover until ready to use.
Heat half of a gas or charcoal grill to high (about 400°F) and the other half to low (about 300°F). Divide dough in 1/2 and roll into 2 rounds about 1/4 inch thick and 10 inches in diameter. Brush the top of 1 round with olive oil and sprinkle with salt.
Lay dough oiled side down on the hotter half of the grill and brush the top with oil and sprinkle with salt. Grill without moving until grill marks form on the bottom of the dough, about 2 minutes.
Flip dough with a spatula or tongs to the cooler half of grill. Spread 1/2 of the sauce evenly over the dough, sprinkle 1 tablespoon of the Parmesan cheese over the sauce, then top with 1/2 of the peppers, 1/2 of the sausage, and 1/2 of the mozzarella. Cover and grill, rotating if necessary to avoid any hot spots, until dough is lightly charred and cheese is melted, about 8 to 10 minutes.
Transfer pizza to a cutting board, sprinkle 1 tablespoon more of the Parmesan over top, drizzle with desired amount of chile oil, slice, and serve. Repeat with second round of dough and remaining toppings.