Place chicken and flour in a large resealable plastic bag; seal bag and shake to coat. Heat 2 teaspoons olive oil in a large skillet over medium heat. Shake excess flour off chicken; cook and stir in hot oil for 4 to 5 minutes each side, or until golden brown and cooked through (juices run clear). Remove from skillet and place in a medium bowl; set aside.
Bring a large pot of lightly salted water to a boil. Add spaghetti and cook for 8 to 10 minutes or until al dente; drain, reserving 2/3 cup cooking water, and return pasta to pot. Set aside pasta and cooking water.
Wipe skillet with paper towel. Heat 1 teaspoon oil in skillet over medium heat. Add green bell pepper, red bell pepper, yellow bell pepper, onion, and garlic and cook and stir for 3 minutes. Cover, reduce heat to low and cook 3 minutes more or until vegetables are tender.
Stir in Alfredo sauce, cover and heat for 1 to 2 minutes. Remove from heat and add to reserved pasta in pot, then add reserved cooking water and chicken. Toss to mix, pour into serving bowls and sprinkle with fresh chopped parsley.