Whisk peanut butter, soy sauce, lime juice, rice vinegar, honey, sesame oil, garlic, ginger, sriracha, and warm water until smooth.
Toss chicken with about two-thirds of the sauce. Season with salt and pepper to taste.
Combine cabbage, carrots, cucumber, green onions, and cilantro in a bowl. Drizzle with remaining sauce and toss to coat.
Warm tortillas until pliable in a microwave or dry skillet.
Layer lettuce on each tortilla. Spoon on chicken and a handful of slaw. Sprinkle with chopped peanuts.
Roll up tightly like a burrito, tucking in the sides. Slice in half and serve.