Make Peanut Dressing: In a medium bowl, whisk together peanut butter, soy sauce, brown sugar, rice wine vinegar, minced garlic, minced ginger, and sriracha sauce until smooth. Add water if needed for desired consistency.

Prepare the Filling: In a large mixing bowl, combine chicken, coleslaw mix, grated carrots, chopped peanuts, and cilantro. Mix until well distributed.

Dress the Filling: Drizzle the peanut dressing over the filling and gently toss with tongs or a spoon until well coated. Let sit for 3-5 minutes.

Warm Tortillas: Wrap tortillas in a damp paper towel and microwave for 30 seconds until warm.

Assemble Wraps: Place filling in the center of each tortilla, fold sides inwards, and roll tightly from the bottom up. Serve immediately.