Whisk together peanut butter, low-sodium soy sauce, brown sugar or honey, rice apple vinegar, minced garlic, minced ginger, and sriracha sauce in a small bowl. Add water if a thinner consistency is desired.
Combine cooked and chopped chicken breasts with coleslaw mix, grated carrot, chopped cilantro, and roasted peanuts. Drizzle the prepared dressing over the mixture and toss gently.
Heat the tortillas in the microwave for about 30 seconds to soften them.
Divide the filling evenly among the warmed tortillas and wrap each one tightly. Serve immediately.