For the chicken:
Place the chicken in a large stockpot along with the onions, celery, sugar, kosher salt, black pepper, and vinegar. Pour in enough chicken stock to cover the chicken breasts. Stir in the concentrated chicken base, partially cover and cook over medium heat until the stock comes to a gentle boil.
Reduce the heat to medium-low and continue simmering until the chicken is cooked through, about 45 minutes to an hour depending on the size of the chicken breasts. Turn off the heat and leave the chicken in the hot stock for 15 to 20 minutes. Remove the chicken from the stock and set aside to cool. When the chicken is cool enough to handle, remove the chicken from the bone and tear or cut it into bite-size pieces.
Raise the heat on the stock back to medium.
For the stew:
Add the butter beans, tomatoes, diced potatoes, whole kernel corn, (the cream corn goes in last) kosher salt, black pepper, and sugar to the reserved stock. Gently break up the tomatoes in the stew. Reduce the heat to medium-low, cover and cook until the potatoes are tender, about 45 minutes.
While the stew is cooking, fry the bacon in a skillet until crisp about 10 to 12 minutes. Set aside to drain on a paper towel.
Once the potatoes are tender, add the bacon along with the cream corn. In a small jar, mix the flour with the cold water, shaking well to make sure there are no lumps. Pour the flour and water mixture in and stir to blend into the stew. Cook for an additional 30 minutes, giving the flour time to cook, slightly thickening and binding the stock. Add additional kosher salt and pepper to taste if needed.