In a skillet set over medium-high heat, add olive oil, garlic and anchovy fillets. Cook, smashing anchovies with a fork to help them dissolve. Add capers and continue to stir. Add tomatoes and use a wooden spoon to crush in the pan. Reduce heat to medium, stir in chili flakes, and allow sauce to simmer for about 5 minutes.
Add cooked linguini to sauce and toss to combine. Garnish with parsley before serving.