Microwave potatoes until translucent, about 7 minutes, then drain.
Mix mayonnaise, lime zest, ¼ teaspoon salt, and chili powder; coat chicken with ¾ of this mixture. Toss potatoes with remaining mayonnaise mixture and salt.
Grill chicken and potatoes until browned and cooked through, about 12-16 minutes. Toast rolls, then assemble sandwiches with avocado, chicken, slaw, and top with roll.