In a small bowl, stir together first 6 ingredients. Place chicken in a slow cooker and sprinkle spice mixture on top of chicken.
Whisk together Coke and next 5 ingredients in a medium bowl. Carefully pour mixture between chicken pieces so as to not wash the spice mixture off the chicken.
Place a lemon slice on top of each piece of chicken.
Cover and cook on HIGH 5 hours (or on LOW 6 1/2 to 7 1/2 hours).
Remove chicken from slow cooker. Discard lemon slices, chicken skin, and chicken bones. Using 2 forks, shred chicken. Skim fat from sauce in slow cooker. Return chicken to sauce.
For Pickled Peppers and Onions, Soak onions in ice water 10 minutes to remove some of their bite. Drain.
Bring vinegar, sugar, salt, and red pepper flakes and 1 cup water to boil in a small saucepan. Stir occasionally to help dissolve the sugar.
Place onions and peppers in a large Mason jar and pour hot vinegar mixture over them. Let stand uncovered on the counter for 1 hour. Cover and chill 24 hours.
For the cornbread: Preheat oven to 425 degrees. Stir together first 4 ingredients in a large bowl. Make a well in center.
In a medium bowl, whisk together eggs, mashed sweet potato, sour cream, and melted butter. Add into well in cornmeal mixture. Stir just until the cornmeal is moistened.
Spoon batter into lightly greased 9-inch square pan. Bake 35 minutes, or until golden.
For the Slaw: Whisk together all ingredients except coleslaw mix in a large bowl. Stir in coleslaw mix and chill at least 30 minutes.
To assemble. cut cornbread into rectangles and then slice each piece. Top bottom half with pulled chicken, then pickled peppers and onions and coleslaw.
Notes
The Pickled Peppers and Onions need to be made 24 hours in advance of serving.