Preheat the oven to 350 degrees F. Place the chicken in a medium saucepan and add 2 cups water, the okra brine, large scallion pieces and dill sprigs. Bring to a boil over high heat. Reduce the heat to a simmer and partially cover. Simmer until the chicken is just cooked through, about 15 minutes.
Meanwhile, toss the coleslaw mix, pickled okra and the chopped scallions and dill in a medium bowl. Add 2 tablespoons vinegar and 1 tablespoon olive oil, season with salt and pepper and toss; set aside. Brush the buns with the remaining 1 tablespoon olive oil; place on a baking sheet and bake until lightly toasted, about 5 minutes.
Reserve 1/2 cup poaching liquid, then drain the chicken and transfer to a cutting board. Shred the chicken with 2 forks and return to the pot. Add the chili sauce, molasses, mustard, the remaining 1 tablespoon vinegar and 1/4 cup of the reserved poaching liquid. Cook over medium heat, stirring, until warmed through, 2 to 3 minutes, adding the remaining poaching liquid as needed if the chicken is too dry. Pile the pulled chicken on the buns and serve with the slaw.