Combine the San-J No Soy Tamari with vinegar, sesame oil, and 1–2 teaspoons sriracha. Set aside.
Combine mayonnaise with 1–2 teaspoons sriracha. Set aside.
Heat oil in a large skillet over medium-high heat. Add the ginger and garlic and cook, stirring for 30 seconds. Add the chicken, salt, and pepper and cook until no longer pink, about 5 minutes. Add the coleslaw and carrots and cook, stirring frequently, until the vegetable are crisp and tender, 4-5 minutes. Add the sauce and cook stirring for 30–45 seconds. Divide mixture into 4 bowls, drizzle with spicy mayonnaise, and top with green onions and sesame seeds.