Position a rack in the upper third of the oven and preheat to 450 degrees F. Whisk 1/4 cup vinegar, 1 tablespoon sugar and the chili powder in a shallow microwave-safe dish. Add the onions, separating them into rings. Cover with plastic wrap and microwave until crisp-tender, 3 to 5 minutes. Toss to coat the onions with the liquid, then let cool.
Meanwhile, whisk 1/3 cup mayonnaise, the cilantro and the remaining 2 tablespoons vinegar and 1 tablespoon sugar in a large bowl. Add the cabbage, jalapenos, 1 teaspoon salt, and pepper to taste and toss. Refrigerate the slaw until ready to serve.
Whisk the remaining 2/3 cup mayonnaise and 1 tablespoon liquid from the pickled onions in a shallow dish. Put the crushed chips in another dish. Coat a baking sheet with cooking spray. Dip the chicken in the mayonnaise mixture and then in the chips; place on the baking sheet. Mist the chicken with cooking spray. Bake until crisp and cooked through, 10 to 12 minutes. Serve with the slaw and onions.