Fill a 10-quart pasta pot with 7 quarts of salted water and bring to a boil over high heat.
Heat a long-handled 14-inch braising pan over medium heat. Add the olive oil with the garlic and cook, stirring, until golden. Add the clams and cook, stirring, for 1 minute. Add the wine, clam juice, tomatoes, and red pepper flakes and stir. Cover, reduce the heat to a simmer, and cook until the clams open and the liquid has reduced and thickened slightly, about 5 minutes.
Add the pasta to the boiling water, stir, and cover until it returns to a boil. Uncover and boil the pasta until al dente. Drain, saving ¼ cup of the pasta water.
Add the pasta to the sauce and toss in the parsley, a pinch of salt (only a small amount since the clams are already naturally salty), and pepper. Toss together until all the pasta is evenly coated. If the sauce is too thick, thin by adding some of the reserved pasta water a little at a time. Cook over low heat 1 minute. Serve immediately.