Heat the vegetable oil in a large (8-quart) soup pot over medium heat. Add the onions and sauté until tender, about 5 minutes. Add the garlic and red pepper flakes and sauté until fragrant, about 1 minute.
Add all the BBQ sauce and 1/2 cup chicken broth. (If your BBQ sauce is thin, skip adding broth at this time). Cook, stirring frequently, until the sauce thickens, reduces, darkens, and a fond forms on the bottom of the pot. The sauce should be about as thick as tomato paste. This will take 15 to 20 minutes.
Add all remaining chicken broth. Scrape the bottom of the pot to release any browned bits. Add the potatoes, tomatoes, Worcestershire, mustard, salt and pepper. Bring to a boil over medium-high heat. Reduce the heat to low, cover and simmer, stirring occasionally until the potatoes are just tender, about 15 minutes.
Increase the heat to medium and stir in all remaining ingredients: chicken, pork, vinegar, cream-style corn, frozen corn, okra and lima beans. Cover and simmer for 30 minutes, stirring occasionally, or until the vegetables are tender and the stew is heated through. (Add up to 1 cup of water or additional broth if desired)
Check seasonings and add additional vinegar (1 to 2 tablespoons) salt and pepper. Serve with hot sauce and cornbread if desired.