Place the chicken in a slow-cooker on low setting. Place all remaining ingredients in a bowl and stir to combine. Slather the sauce over the chicken pieces. Close the lid of the slow cooker and cook on HIGH for 4-5 hours or on LOW for 6-8 hours. Make there is enough liquid on the bottom at all times to prevent burning and add a little water as needed.
Transfer the chicken to a plate, remove and discard the skin, and shred the chicken. Return the shredded chicken to the juices in the slow-cooker and stir to coat the chicken. If it's too dry, add a little more water. Add salt to taste. Let the chicken absorb the juices a little longer, at least 20 minutes, and keep warm until ready to serve.
Toast some whole wheat hamburger buns, use a slotted spoon the remove some of the excess juices of the chicken and place some of the chicken mixture on the bottom half of the bun, top with some extra mango chutney and shredded red cabbage and serve immediately. If desired, place some lettuce on the bottom halves of the hamburger buns before adding the chicken.