Whisk together teriyaki marinade, soy sauce, ginger, brown sugar, red pepper flakes, and black pepper in a large glass or ceramic bowl until well combined. Add chicken and toss to evenly coat. Cover the bowl with plastic wrap and marinate in the refrigerator for 5 hours.

Heat a wok over medium-high heat. Add scallions, garlic, and sesame oil; stir-fry for about 1 minute. Add broccoli, snow peas, and bell pepper; stir-fry for 2 minutes more. Add stir-fry sauce and mix until vegetables are coated.

Remove chicken from marinade and shake off excess; discard remaining marinade. Add chicken to vegetables in the wok and stir-fry until chicken is no longer pink in the center and the juices run clear, about 5 minutes. An instant-read thermometer inserted into the center of chicken should read at least 165 degrees F (74 degrees C).