In a 5- to 6-quart pan over high heat, bring about 4 quarts water to a boil. Add spaghetti and cook, stirring occasionally, until barely tender to bite, about 10 minutes.
Meanwhile, in a 10- to 12-inch frying pan over medium-high heat, stir garlic in olive oil often until fragrant (do not brown), 1 to 2 minutes. Add wine, clam juice, and reserved liquid from clams and boil until reduced to about 1 cup, 6 to 8 minutes. Add clams and stir occasionally until hot, 1 to 2 minutes.
Drain spaghetti. Add to clam sauce along with parsley and chili flakes; mix, and add salt to taste. Divide equally among four wide bowls.