Preheat a grill to medium high. Toss the chicken with 1 tablespoon olive oil. Pound each chicken breast between 2 pieces of plastic wrap with the flat side of a meat mallet or heavy skillet until 1/4 to 1/2 inch thick. Brush the chicken on both sides with the remaining 1 tablespoon olive oil and season with the oregano, salt and pepper.
Brush the grill grates with olive oil. Grill the chicken until cooked around the edges, about 3 minutes. Flip and spread the top of the chicken with the pizza sauce. Top with the mozzarella slices, then the tomato slices. Cover and grill until the chicken is cooked through and the cheese is slightly melted, 3 to 4 minutes.
Remove the chicken pizzas from the grill. Sprinkle with salt, pepper, basil and red pepper flakes.