Bring a large pot of lightly salted water to a boil. Cook bow-tie pasta at a boil, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain.
Heat oil in a skillet over medium-high heat. Add chicken strips; cook and stir until no longer pink in the center and the juices run clear, 5 to 7 minutes. Transfer to a plate lined with paper towels.
Reduce heat under skillet to medium; add onion, orange bell pepper, red bell pepper, garlic, dried basil, and red pepper flakes to skillet. Cook and stir until onions are translucent and peppers are softened, 3 to 5 minutes. Add tomato sauce; heat for about 2 minutes. Add chicken; cook for another 2 to 3 minutes. Portion cooked pasta into bowls; spoon chicken and sauce mixture on top.
