Make sesame vegetables: In a heavy skillet heat vegetable oil over moderate heat until hot but not smoking and cook bell pepper, mushrooms, scallions, and red pepper flakes, stirring, until vegetables are golden and cooked through, about 5 minutes. Toss vegetables with sesame oil and salt and pepper to taste.
Make chicken: In a small bowl combine soy sauce, Sherry, brown sugar, garlic, gingerroot, and salt and pepper taste and stir until sugar is dissolved. Gently pound chicken between 2 sheets of plastic wrap until about 1/4 inch thick. In a large sealable plastic bag marinate chicken in soy sauce mixture, turning occasionally, 25 minutes.
In a heavy skillet heat oil over moderate heat until hot but not smoking. Remove chicken from marinade, letting excess drip off and reserving marinade, and cook until browned and cooked through, 3 to 4 minutes on each side. Transfer chicken to plate and keep warm. Pour reserved marinade through a sieve into skillet and boil until reduced to about 2 tablespoons.
Drizzle chicken with sauce and serve with sesame vegetables.