In a small bowl, whisk together soy sauce, oyster sauce, cornstarch, water, black pepper, and crushed red pepper flakes. Set the sauce mixture aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken strips to the skillet and stir-fry for 5 to 6 minutes until cooked through and lightly browned. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of vegetable oil.
Add the minced garlic and ginger, and stir-fry for 30 seconds until fragrant.
Add the sliced red and yellow bell peppers, julienned carrot, broccoli florets, and snap peas to the skillet. Stir-fry for 4 to 5 minutes until the vegetables are tender-crisp.
Return the cooked chicken to the skillet with the vegetables.
Pour the prepared sauce over the chicken and vegetables. Stir well to combine and cook for an additional 2 minutes until the sauce thickens and coats all ingredients.
Remove from heat and stir in the sliced green onions.
Transfer the stir fry to a serving dish and sprinkle with toasted sesame seeds before serving.