In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the garlic, ginger, red bell pepper, broccoli, and snap peas. Stir-fry for about 3-4 minutes, until the vegetables are tender-crisp.
In a bowl, whisk together the peanut butter, soy sauce, honey, rice vinegar, sesame oil, and red pepper flakes until smooth.
Return the cooked chicken to the skillet with the vegetables. Pour the peanut sauce over the chicken and vegetables, stirring to coat everything evenly. Cook for an additional 2-3 minutes until heated through.
Serve the stir-fry over cooked rice or noodles. Garnish with chopped green onions and crushed peanuts if desired.