Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1/2 cup cooking water, then drain.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the garlic, red pepper flakes and 1/2 teaspoon salt; cook until the garlic is lightly golden, about 2 minutes. Add the clams, scallops and lemon zest. Cook, stirring, until the scallops are just cooked through, about 2 minutes.
Add the pasta, reserved clam juice, lemon juice, parsley and parmesan to the skillet; cook, tossing to coat, 1 minute, adding the reserved cooking water as needed to loosen. Season with salt and pepper. Drizzle each serving with olive oil and top with more parmesan.