Prepare a gas grill for direct-heat cooking over medium-high heat; see Grilling Procedure . Mince and mash garlic to a paste with a pinch of salt, then whisk with 2 tablespoons oil and red-pepper flakes in a large bowl. Brush zucchini with remaining tablespoon oil and season with 1/4 teaspoon each of salt and pepper. Oil grill rack, then grill zucchini, cut sides down first, covered, turning once, until just tender, 6 to 8 minutes. Slice zucchini crosswise 1/4 inch thick, then immediately toss with garlic oil. Stir together 1/2 cup cheese, walnuts, and 1/2 teaspoon pepper and set aside. Cook fettuccine in a pasta pot of salted boiling water until al dente. Reserve 1/2 cup cooking water, then drain pasta. Toss pasta with zucchini, remaining 1/4 cup cheese, and reserved cooking water. Serve sprinkled with walnut mixture.