In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the diced chicken and season with salt and pepper. 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 minced garlic, ginger, and crushed red pepper flakes. Sauté for about 30 seconds until fragrant.
Add the diced red and green bell peppers to the skillet and stir-fry for about 3-4 minutes until they are tender-crisp.
Return the cooked chicken to the skillet. In a small bowl, whisk together the soy sauce, rice vinegar, hoisin sauce, cornstarch, and water. Pour this sauce over the chicken and vegetables, stirring to combine.
Add the peanuts and sliced green onions to the skillet. Cook for an additional 2-3 minutes, stirring frequently, until the sauce thickens and everything is well coated.
Serve the Kung Pao chicken over the cooked white rice.