In a small bowl, whisk together flour, vegetable broth, vinegar, soy sauce, and brown sugar (if desired), to a smooth paste; set aside.
Heat the oil in a large skillet over medium-high heat; add onion and gingerroot and sauté for 30 seconds. Add carrots and bell pepper and cook for an additional 4 to 5 minutes. Add cubed flounder
and cook, stirring often, for 5 minutes.
Give reserved broth mixture a stir and add to skillet; cook and stir until sauce has thickened and flounder is cooked through.