Heat oil in a skillet over medium heat. Lightly coat the chicken in flour and season with salt. Cook until golden on both sides and fully cooked through. This step locks in moisture and gives the chicken a light crust.
Melt butter in a saucepan and sauté onion and garlic until fragrant. Add white wine and let it reduce slightly, then pour in chicken stock, lemon juice, parsley, and red pepper flakes. Remove from heat and whisk in remaining butter until smooth.
Bring a large pot of salted water to a boil and cook the angel hair pasta until just tender. Drain and reserve some pasta water to adjust the sauce later if needed.
In the same skillet, sauté the bell peppers and red onion until softened but still colorful. Avoid overcooking so they retain texture.
Add the cooked pasta to the vegetables and pour over the scampi sauce. Toss gently, adding reserved pasta water if needed. Top with chicken and finish with Parmesan cheese if desired.