Preheat oven to 350°F. Heat oil in large, oven-safe nonstick skillet over medium heat. Add shallot, garlic and red pepper flakes; cook, stirring a few times, until vegetables soften, 2-3 minutes.
Add anchovy paste and cook, stirring, until it melts into pan, about 1 minute. Add tomatoes and tomato paste; reduce heat to medium-low and simmer until sauce thickens, about 5 minutes. Stir in olives and capers; remove from heat.
Nestle salmon fillets into sauce; spoon some sauce over salmon. Cover skillet; bake until fish is just opaque in center, about 10-12 minutes.