Preheat oven to 425 degrees F, with the rack placed in upper third. Line a rimmed baking sheet with aluminum foil; set aside.
In a food processor, place bread, Parmesan, oil, and a pinch salt and black pepper. Pulse until coarse crumbs form; transfer to a shallow bowl. Place flour in a another shallow bowl; season with salt and pepper. Place egg white in a another shallow bowl, and beat with a fork.
Dip top side of a chicken breast in flour, shaking off excess. Dip same side in egg white, letting excess drip off, then in breadcrumbs to coat. Do not bread the other side of the chicken. Repeat with remaining chicken and transfer, breaded side up, to prepared baking sheet. Bake until breadcrumbs are crisp and browned, 8 to 10 minutes. Remove from oven; top with mozzarella. Continue baking until chicken is cooked through and cheese is lightly browned, 2 to 4 minutes.
Meanwhile, in a large skillet, place tomatoes, breaking them up with a fork or wooden spoon. Add garlic, Italian seasoning and red pepper flakes; season with salt and pepper. Bring to a boil, reduce to a simmer, and cook until sauce has thickened, 6 to 8 minutes. Serve chicken with the tomato sauce.