Heat 2 Tbsp oil in a large saucepan over medium-high heat. Add half the garlic and cook, stirring occasionally, until pale golden, 1–2 minutes. Add pepper flakes and cook for 10 seconds. Add clams and white wine; cover and boil just until clams open, about 6 minutes. Drain, reserving clam broth; set broth and clams aside.
Meanwhile, bring a large pot of salted water to a boil. Add pasta and cook until almost al dente, about 8 minutes. Drain pasta, reserving 1/2 cup cooking liquid.
Heat remaining 4 Tbsp oil in a large skillet over medium-high heat. Add remaining garlic; cook, stirring often, until pale golden, about 2 minutes. Add reserved clam broth and pasta liquid. Bring to a boil; boil until sauce is emulsified, about 1 minute. Add pasta and cook, stirring often, until sauce begins to cling to the pasta but is still loose, about 3 minutes. Stir in parsley, then gently stir in clams. Divide among bowls.