Mix chicken, chipotle-flavored olive oil, soy sauce, and red pepper flakes together in a bowl.
Heat garlic-flavored olive oil in a wok or large skillet over medium heat; cook and stir snap peas, onion, red bell pepper, orange bell pepper, and garlic until partially tender, about 5 minutes. Add white wine, garlic pepper seasoning, and ground ginger to vegetable mixture; cook and stir until chicken is almost cooked through, about 5 minutes.
Whisk cornstarch and water together in a small bowl until dissolved.
Mix mushrooms and cornstarch mixture into chicken mixture; cook and stir until sauce is thickened and chicken is no longer pink in the center, about 5 minutes more.