Coat a large Dutch oven with cooking spray; add oil, and place over medium heat until hot. Add chicken and cook 3 minutes on each side or until lightly browned. Remove pan from heat. Drizzle 3 tablespoons vinegar over chicken and sprinkle with salt, 8 teaspoon thyme, and garlic. Add remaining 3 tablespoons vinegar, carrots, and next 3 ingredients to pan. Cover and bake at 400 degrees F for 40 minutes or until chicken and vegetables are tender. Remove chicken and vegetables with a slotted spoon, reserving cooking liquid; set aside. Place flour in a bowl. Gradually add 4 cup water, stirring with a wire whisk until blended; add to reserved cooking liquid. Add remaining 8 teaspoon thyme, broth, and pepper; stir well. Bring mixture to a boil over medium-high heat and cook 4 minutes or until thickened and bubbly, stirring constantly. Spoon chicken mixture and gravy into separate airtight containers; store in freezer up to 2 weeks. To serve, thaw in refrigerator. Place chicken mixture in a Dutch oven; cover and bake at 350 degrees F for 30 minutes or until thoroughly heated. Spoon gravy into a small saucepan; cook over medium-low heat 7 minutes or until thoroughly heated, stirring occasionally with a wire whisk. Serve with chicken mixture.