Heat coals or gas grill for direct heat. Cut four 18x12-inch pieces of heavy-duty foil. Place chicken breast half on each piece of foil. Top with potatoes, carrots and frozen green beans. In small bowl, mix gravy and flour until well blended. Drizzle over chicken mixture. Sprinkle with paprika and thyme.
Fold foil over chicken and vegetables so edges meet. Seal edges, making tight 1/2-inch fold; fold again. Allow space on sides for circulation and expansion.
Cover and grill packets over medium heat 30 to 40 minutes, rotating packets 1/2 turn after 15 minutes, until juice of chicken is no longer pink when centers of thickest pieces are cut and vegetables are tender. Place packets on plates. Cut large X across top of each packet; fold back foil. Sprinkle with parsley.