Place the chicken breasts in the slow cooker. Add the barbecue sauce, brown sugar, smoked paprika, garlic powder, salt, and black pepper. Stir to coat the chicken evenly.
Cover and cook on low for 6 hours or until the chicken shreds easily with two forks. Shred the chicken directly in the slow cooker and stir it into the sauce.
In a large bowl, combine the shredded cabbage, apple cider vinegar, olive oil, honey, salt, and celery seed. Toss well and let the slaw sit while the chicken finishes cooking.
Toast the sandwich buns if desired. Pile the pulled chicken onto the bottom halves of the buns and top each with a generous scoop of vinegar slaw.