Place whole-wheat flour in a shallow dish. Sprinkle trout with pepper and ½ teaspoon of the salt. Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high. Dredge 2 trout fillets in flour; shake off excess. Place trout, flesh side down, in skillet, and cook until browned, about 3 minutes. Turn and cook until fish flakes easily with a fork, about 2 minutes. Remove trout from skillet, and cover to keep warm. Repeat with remaining 1 tablespoon oil, flour in dish, and trout fillets. Remove skillet from heat.
Whisk together stock and all-purpose flour in a small bowl. Return skillet to medium-high. Add wine to skillet, and cook until reduced by half, about 1 minute. Stir in stock mixture, and cook until slightly thickened, about 2 minutes. Remove from heat. Stir in capers, lemon juice, butter, parsley, and remaining ½ teaspoon salt. Serve fillets with sauce.