Mix flour with ¼ tsp. salt and pepper. Pat fillets dry and coat in flour mixture.
Heat a 12-inch heavy skillet over medium heat. Add almonds to skillet and cook, stirring frequently until almonds are browned, set aside. Add 2 Tbsp. butter to skillet and heat until foam subsides. Place fish skin side down and cook until golden brown, about 4 minutes. Turn fish over and heat until just cooked through, 1 to 2 minutes more. Transfer to a plate with a slotted spatula and keep warm, loosely covered with foil.
Add remaining 2 tbsp. butter, lemon juice and reserved 1/8 tsp. salt to skillet. Swirl butter until fully melted than pour sauce over fish. Top with parsley and toasted almonds.