Cut off a 1 1/2-inch piece of the baguette and pulse in a food processor to make breadcrumbs. Add the tomatoes and 1/4 teaspoon salt and pulse until the tomatoes are finely chopped but not pureed. Heat 1 1/2 tablespoons olive oil in a medium skillet over medium heat; add the garlic and cook until just golden, about 1 minute. Add the red pepper flakes and tomato mixture and bring to a simmer; cook until the sauce thickens slightly, 8 to 10 minutes.
Meanwhile, preheat a grill to medium high. Toss the chicken with the remaining 1/2 tablespoon olive oil, the oregano and 1/4 teaspoon salt. Split the remaining baguette in half lengthwise and then cut in half to make 4 pieces.
Grill the bread, cut-side down, until lightly toasted. Grill the chicken until cooked through, about 5 minutes per side, topping with the mozzarella and covering during the last 2 minutes.
Spoon some tomato sauce onto the bread pieces and top with half of the parmesan. Top each with a chicken breast, then the remaining sauce. Sprinkle with basil and the remaining parmesan.