I would not use Blu-Kote for punctures nor burns. However, like all off label products that we use on our chickens including Blu-Kote, common sense regarding proper usages/dosages should take precedence. I use Blu-Kote for minor scrapes, scratches and small cuts as well as for hiding blood so that the injured chicken wont get picked/pecked on for said injuries by the others.
Most likely why you dont use Blu-Kote on punctures and burns is because of the isopropyl alcohol which would cause stinging/burning. But it's main purpose is used as a quick drying agent in the product.