Bring a large pot of salted water to a boil and add the angel hair pasta; cook until it is just short of al dente. Reserve 1 cup of the pasta water and drain the rest.
While the pasta water is heating, heat a large skillet on medium and pour in 2 Tablespoons of vegetable oil. In a shallow dish, combine flour with a pinch of salt and dredge the chicken tenderloins, shaking off excess flour.
Once the oil is hot, cook each piece of chicken until golden on both sides, about 5 to 7 minutes per side, using additional oil as necessary. Remove chicken and set aside.
In a medium saucepan over medium heat, melt 2 Tablespoons of butter. Add diced yellow onion and minced garlic, cooking gently for about 3 minutes until softened but not browned.
Pour in the white wine, letting it simmer for 2 minutes to reduce and evaporate the alcohol, scraping the pan to loosen any browned bits.
Add chicken stock, lemon juice, dried parsley, and red pepper flakes, then let the mixture simmer for 5 minutes to meld flavors.
Take the pan off heat and whisk in the remaining 8 tablespoons of butter until the sauce is smooth and glossy, then set the sauce aside.
Return the large pot to the stove and heat 1 Tablespoon of oil over medium heat. Add the sliced bell peppers and red onion, sautéing for 3 to 5 minutes just until they begin to soften.
Add the pasta and prepared scampi sauce to the pot with the vegetables, carefully tossing everything together to coat the pasta without breaking it. Adjust seasoning with salt and pepper, and use reserved pasta water to loosen the sauce if needed.
Serve the pasta topped with the cooked chicken pieces and sprinkle with freshly grated Parmesan cheese if desired.