In a small bowl, blend cornstarch with sherry, soy sauce, garlic, brown sugar & red pepper flakes, then set aside.
In a large nonstick skillet, warm 2 teaspoons of the oil over medium-high heat until hot, but not smoking, then add the chicken, stir-frying until just barely cooked, about 2 minutes. With a slotted spoon, transfer the chicken to a plate & cover loosely to keep warm.
Add 2 teaspoons of the oil to the skillet & heat, then add the onion, stir-frying until softened, about 3 minutes.
Add the remaining 2 teaspoons of the oil as well as the cabbage & bell peppers & stir-fry until crisp-tender, about 2 minutes.
Add reserved sherry mixture to the skillet along with the chicken (& any juices that have collected on the plate) & cook over medium-high heat until the sauce thickens & the chicken is cooked through, about 3 minutes.