Heat the olive oil in a large skillet over medium heat. Add the garlic and red pepper flakes and cook until the garlic is just golden, about 1 minute. Crush the tomatoes into the skillet with your hands and add the juice. Add 1/2 teaspoon salt and simmer, stirring occasionally, until the sauce is slightly thickened, about 15 minutes. Add the zucchini and cook until crisp-tender, about 5 minutes. Season with salt.
Meanwhile, bring a large pot of salted water to a boil. Add the capellini and cook as the label directs. Drain and add to the sauce along with the basil; toss to coat. Top with parmesan.