Butterfly each chicken breast to create four even pieces.
Season the chicken with smoked paprika, garlic powder, salt, black pepper, cayenne pepper, and olive oil.
Heat a skillet over medium-high heat and cook the chicken for 3–4 minutes.
Flip the chicken and brush the cooked side generously with BBQ sauce.
Continue cooking until the chicken is fully cooked through.
Transfer the chicken to a cutting board with the BBQ-coated side facing down. Brush the other side with more BBQ sauce and let it rest for 5 minutes.
Slice the chicken against the grain into thin strips.
In a small bowl, whisk together mayonnaise, sour cream, Dijon mustard, apple cider vinegar, sugar, salt, and pepper.
Toss the dressing with the grated carrot, sliced cabbage, and onion until evenly coated.
Lay a tortilla flat and add a layer of spinach, followed by the coleslaw and sliced BBQ Chicken Wraps filling.
Fold the sides inward and roll tightly like a burrito.
Slice in half and serve immediately.