Marinate the chicken: In a small bowl, whisk together the soy sauce, ginger, canola oil, hoisin sauce, sesame oil, sriracha, and kosher salt. Place the chicken breasts in a resealable plastic bag or shallow dish and pour the marinade over the chicken. Seal the bag or cover the dish and refrigerate for at least 30 minutes or up to 2 hours to allow the flavors to develop.
Cook the chicken: Preheat a grill or grill pan over medium-high heat. Remove the chicken from the marinade and grill for 5-6 minutes on each side, or until the chicken is cooked through and reaches an internal temperature of 165°F (75°C). Set aside to cool slightly, then slice the chicken thinly.
Prepare the salad: In a large mixing bowl, toss together the napa cabbage, carrots, scallions, and cilantro leaves. Drizzle the rice wine vinegar over the salad and toss gently to combine.
Assemble the salad: Place the vegetable mixture on a serving platter or in a large bowl. Top with the sliced chicken, crispy wontons, slivered almonds, and sesame seeds.
Serve: Serve the salad immediately while the chicken is still warm and the wontons are crispy. You can add extra rice vinegar or sesame oil for additional flavor, if desired.