Whisk soy sauce and ginger together in a small bowl. Place chicken in mixture and marinate in refrigerator for about one hour. After marinating, prepare grill for direct grilling over medium-high heat. Place the chicken on the grill directly over the fire and cook until the juices run clear and the chicken is cooked through, about 5 to 8 minutes on each side.
To make the dressing:
Combine soy sauce, honey, lime juice, and red pepper flakes in a small bowl. Whisk until smooth. Add the peanut butter and water and whisk again until smooth and creamy. Add more water as necessary until desired consistency is reached.
To assemble the wraps:
Divide ingredients into 4 servings, spread over wraps, layer with chicken and top with dressing. Fold the bottom edge of the wrap up. Fold the sides of the wrap inward and then roll the wrap up tightly to enclose all of the fillings. Serve immediately.