Whisk 2 tablespoons all-purpose flour, ½ teaspoon table salt, and ¼ teaspoon pepper together in small bowl. Reserve 1 teaspoon flour mixture, then spread remaining mixture in even layer on large plate.

Dry 6 skinless flounder fillets thoroughly with paper towels. Place 3 fillets, skinned side down, into flour mixture on plate to coat 1 side. Shake off excess and transfer to rimmed baking sheet, floured side up.

Heat 1½ teaspoons vegetable oil in 12-inch skillet over medium-high heat until just smoking. Carefully place fillets, floured side down, in pan and cook until bottom is golden brown, about 2 minutes. Remove skillet from heat. Using 2 thin spatulas, gently flip fillets and let stand until second side is opaque, 15 to 30 seconds. Transfer fillets, browned side up, to platter. Wipe out skillet with paper towels and repeat steps 2 and 3 with remaining fillets and 1½ teaspoons oil.

Wipe out skillet with paper towels. Add remaining 1 teaspoon oil and 3 minced garlic cloves and cook over medium heat until fragrant, about 30 seconds. Stir in reserved 1 teaspoon flour mixture and cook for 15 seconds. Add 10 ounces cherry tomatoes, ⅓ cup white wine, ⅓ cup water, ¼ teaspoon pepper flakes, and remaining ½ teaspoon salt and bring to simmer. Cover and cook, stirring occasionally, until tomatoes have burst, about 5 minutes. Uncover and continue to cook, breaking up tomatoes with back of wooden spoon, until sauce has thickened slightly, about 2 minutes.

Off heat, stir in 1 tablespoon chopped oregano. Spoon sauce over fish and serve.