In a large plastic bag, combine the sriracha sauce, honey, lime juice, ground ginger, and a pinch of salt and pepper. Mix together. Add the chicken, coat with the marinade, and refrigerate for 15-20 minutes or up to 3 hours.
The chicken can then be cooked on the grill, in the oven, or in a skillet on top of the stove. Cook the chicken until it is well done and no longer pink inside. When it's slightly cool but still hot, cut it into cubes.
While your chicken is marinating, prepare the sour cream sauce by whisking together the sour cream, cilantro, lime juice, honey, sriracha, and a pinch of salt. Set aside.
Add the hot chicken to the taco shells. Top with cheese, mixed greens, green onions, and avocado; then drizzle with sour cream sauce. (Drizzling with additional sriracha is optional.) Serve immediately.