In a medium bowl, whisk together the peanut butter, soy sauce, honey, rice vinegar, sesame oil, garlic, ginger, and red pepper flakes until smooth. Set aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the chicken pieces and cook for about 5-7 minutes, or until browned and cooked through.
Add the sliced bell peppers and broccoli to the skillet. Stir-fry for an additional 3-4 minutes, until the vegetables are tender-crisp.
Pour the peanut butter sauce over the chicken and vegetables. Stir well to coat everything evenly. Cook for another 2-3 minutes until the sauce is heated through.
Serve the peanut butter chicken over cooked rice or noodles and garnish with chopped green onions.