In a large skillet over medium heat, combine the shredded chicken, barbecue sauce, apple cider vinegar, smoked paprika, garlic powder, and black pepper. Cook for 4 to 5 minutes, stirring occasionally, until heated through and evenly coated.
In a medium bowl, stir together the coleslaw mix, mayonnaise, apple cider vinegar, honey, dill pickle juice, and salt until lightly coated.
In a small bowl, whisk together the ranch dressing and barbecue sauce until smooth.
Warm the tortillas until soft and pliable.
Divide the iceberg lettuce evenly among the tortillas.
Top with the prepared slaw, tomatoes, red onion, and shredded cheese.
Season lightly with salt and black pepper.
Divide the warm BBQ chicken among the tortillas.
Drizzle the BBQ ranch sauce over the chicken.
Fold in the sides and roll tightly into wraps.
Place the wraps seam-side down in a dry skillet over medium heat and toast for 1 to 2 minutes per side until golden brown and lightly crisp.
Slice in half and serve immediately.