Stir the arugula, parsley, olive oil, capers, lemon zest, lemon juice, salt, and red pepper flakes in a small bowl to blend.
Position an oven rack in the center of oven. Preheat the oven to 375 F.
Mix the parsley, chives, and lemon zest in a small bowl to top the fish.
Coat the salmon fillets all over with the olive oil. Put the fish on a rimmed baking sheet. Sprinkle on both sides with the salt and pepper. Sprinkle the herb topping over the top of the fish fillets, pressing slightly to adhere.
Bake the fish until medium, about 9 to 10 minutes. Transfer 1 fish fillet to each of 4 plates. Spoon the salsa verde alongside. Serve with lemon wedges, if desired.