Preheat oven to 325°.
Remove and discard giblets and neck from chicken. Rinse chicken under cold water; pat dry. Trim excess fat. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Rub thyme, salt, and pepper on breast and drumsticks under loosened skin; place 2 garlic cloves in body cavity. Lift wing tips up and over the back; tuck under chicken. Set aside.
Combine 8 garlic cloves, wine, and half of broth in a shallow roasting pan lined with foil. Place chicken on a rack coated with cooking spray; place rack in pan. Insert meat thermometer into meaty part of thigh, making sure not to touch bone.
Bake at 325° for 1 hour and 45 minutes or until thermometer registers 180°. Discard skin. Place chicken on a platter, reserving pan drippings; set chicken aside. Keep warm.
Place flour in a small saucepan. Gradually add remaining half of broth, stirring with a whisk until blended. Set aside. Place a zip-top plastic bag inside a 2-cup measure. Pour pan drippings into bag; let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off 1 bottom corner of bag. Drain drippings into broth mixture in saucepan, stopping before fat layer reaches opening; discard fat. Bring mixture to a boil; cook 1 minute or until thick, stirring constantly with a whisk. Serve gravy with chicken.