Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally until cooked through but firm to the bite, 4 to 5 minutes. Drain.

Heat oil in a large non-stick pan or wok over medium heat; cook and stir chicken until no longer pink in the center, about 5 minutes. Add celery, red bell peppers, red onion, and carrots; cook and stir until vegetables are slightly tender, about 5 minutes.

Mix chicken broth, soy sauce, cornstarch, garlic powder, and sesame oil in a small saucepan; bring to a boil. Reduce heat and simmer until desired thickness of sauce is reached, 5 to 10 minutes.

Stir peanuts, garlic, and red pepper flakes into chicken-vegetables mixture; cook for 2 minutes more. Pour sauce over chicken-vegetable mixture; add spaghetti and toss to coat.