In a 5- to 6-quart pan over high heat, cook vermicelli in about 3 quarts boiling water just until barely tender to bite, about 7 minutes.
Meanwhile, in a 10- to 12-inch frying pan, combine oil and garlic. Stir over medium-high heat until garlic is soft but not brown, about 1 minute. Mix in anchovies.
Turn heat to high. Add tomatoes, olives, capers, and hot chili flakes to pan and stir until tomatoes are hot, about 3 minutes.
Drain pasta and pour into a large bowl. Spoon tomato sauce over pasta and mix. Add cheese, salt, and pepper to taste.