1. Preheat oven to 325°.
2. Heat a Dutch oven over medium-high heat. Add 2 teaspoons canola oil. Sprinkle the chicken with black pepper and 1/4 teaspoon salt. Place flour in a dish, and dredge chicken. Place 2 leg quarters in pan, and cook for 1 1/2 minutes on each side. Remove from pan. Repeat procedure with 2 teaspoons oil and remaining 2 leg quarters. Remove from pan.
3. Add remaining 2 teaspoons oil to pan. Add garlic; cook for 20 seconds. Add half of kale; cook for 2 minutes. Add remaining half of kale; cook 3 minutes. Stir in tomatoes and broth; bring to a boil. Return chicken to pan. Cover and bake at 325° for 1 hour and 15 minutes. Remove chicken from pan; stir in vinegar. Serve chicken over kale mixture.