In a small bowl, whisk together rice vinegar, soy sauce, sesame oil, vegetable oil, honey, grated ginger, minced garlic, and sriracha. Add the reserved ramen seasoning packet and whisk until completely dissolved. Let dressing sit for 10 minutes.
In a large bowl, combine shredded napa cabbage, red cabbage, julienned carrots, and sliced green onions.
Add the shredded chicken and drained mandarin oranges to the cabbage mixture. Toss gently to distribute evenly.
Right before serving, add the crushed ramen noodles and toasted almonds to maintain maximum crunch.
Pour the dressing over the salad and toss until everything is well coated. Sprinkle with sesame seeds and serve immediately.