Cook angel hair pasta according to package directions until al dente. Drain and toss with 1 tablespoon olive oil to prevent sticking. Set aside.
In a shallow dish, combine ½ cup flour, Italian seasoning, ½ teaspoon salt, and ¼ teaspoon black pepper. Toss chicken pieces in flour mixture, shaking off excess.
Heat 2 tablespoons olive oil and 1 tablespoon butter in a large skillet or Dutch oven over medium-high heat. Add chicken in a single layer and cook until golden brown on all sides, 5-6 minutes total. Remove to a plate and set aside.
Add remaining 2 tablespoons butter to the same pan. Once melted, add sliced bell peppers and red onion. Cook for 4-5 minutes until tender-crisp. Add minced garlic and cook 30 seconds until fragrant.
Pour in white wine to deglaze the pan, scraping up browned bits. Simmer for 2 minutes to reduce slightly. Add chicken broth, heavy cream, and lemon juice. Bring to a gentle simmer and cook 3-4 minutes until sauce thickens.
Return chicken to the pan along with cooked pasta. Toss everything together until well coated in the creamy sauce. Taste and adjust seasoning with remaining salt and pepper.
Garnish with fresh parsley and serve immediately while hot. Enjoy your homemade Olive Garden Chicken Scampi!