What is the proper way to treat a popped burn blister on a child?

Keep covered. The main risk of popped blisters associated with burns is the risk of infection. It is important to keep the area clean, covered with an antibiotic cream, and a dressing. Any loose skin can be carefully trimmed away to prevent it from trapping infection. Please see the doctor if the area is very large, gets red and tender, or has lots of drainage.