Heat the vegetable oil in a large skillet or wok 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 red bell pepper, broccoli, and snap peas. Stir-fry the vegetables for about 3-4 minutes until they are tender-crisp.
Add the minced garlic and ginger to the skillet, cooking for an additional 1 minute until fragrant.
In a small bowl, whisk together the peanut butter, soy sauce, honey, rice vinegar, sesame oil, and red pepper flakes (if using) until smooth.
Return the cooked chicken to the skillet and pour the peanut sauce over the chicken and vegetables. Stir well to coat everything in the sauce and heat through for another 2-3 minutes.
Serve the stir-fry over cooked rice or noodles, garnished with chopped green onions and sesame seeds.