Pound chicken breasts with a meat mallet to 1/4-in. thickness. Sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Place flour in a shallow bowl. Dip chicken in flour to coat both sides; shake off excess., Cook pasta according to package directions for al dente. Meanwhile, in a large skillet, heat 2 tablespoons oil over medium heat. Add chicken; cook 2-3 minutes on each side or until no longer pink. Remove and keep warm., In same pan, heat remaining oil over medium heat; add garlic. Cook and stir 30-60 seconds or until garlic is lightly browned. Add wine to pan; increase heat to medium-high. Cook, stirring to loosen browned bits from pan, until liquid is reduced by half. Stir in lemon juice., Drain pasta, reserving 1/2 cup pasta water; place in a large bowl. Add cheese, 1/3 cup parsley, half of the garlic mixture, and remaining salt and pepper; toss to combine, adding enough reserved pasta water to moisten pasta. Serve with chicken. Drizzle with remaining garlic mixture; sprinkle with remaining parsley. If desired, serve with lemon wedges.