Using a large mixing bowl, add in all the ingredients for the stir fry sauce then mix properly. Reserve a little of the marinade, add in the chicken, toss to coat, cover the bowl and marinate the chicken in the refrigerator for about thirty minutes.
Place a skillet pan over medium heat then add in the oil. Once the oil is hot, add in the onions and cook for about two minutes, add in the broccoli and peppers then cook for a few more minutes until the veggies become crisp-tender, set aside in a foil to keep warm.
Next, still using the same skillet pan over medium heat, add in a little more oil, then heat. Once the oil is hot, add in the chicken and cook for about three to four minutes on both sides until the chicken is cooked through.
Add in the cooked veggies, the rest of the marinade, mushrooms, sesame oil, and red pepper flakes then cook for about three to four minutes until the mushrooms are cooked through. Serve.