Bring 6 quarts water to a boil in a large pot and add 3 tablespoons kosher salt. Meanwhile, combine the oil and garlic in a large pot and cook, stirring, over medium- high heat until the garlic is softened, about 1 minute. Add the wine, red pepper flakes, and clams, cover, and cook, shaking the pot occasionally, until the clams open, about 5 minutes; transfer the clams to a bowl as they open. Remove the pot from the heat.
Drop the pasta into the boiling water and cook until just al dente. Drain, reserving about 1⁄2 cup of the pasta water.