Cook the fettuccini in boiling, lightly salted water until tender, about 8 to 10 minutes. While it cooks, heat the oil in a large skillet over medium to medium-high heat. Add the garlic, anchovies and chili flakes and cook until fragrant, about 1 minute. Mix in tomatoes, olives and capers and simmer the sauce 5 minutes. When cooked, drain the fettuccini well, reserving 1/2 cup of the cooking liquid. Add the reserved cooking liquid and the basil to the sauce and toss to combine.
Note: Bottled, strained tomatoes can be found in the aisle other canned tomato products are sold. Tomato sauce can be substituted.