Burn fellowships are generally open to those trained in General or Plastic surgery (a Pediatric Surgeon would be first trained in General so would obviously be eligible as would a Trauma Surgeon).
If you desire to be a Burn Surgeon, your first stop is either an Integrated Plastics residency or a General Surgery residency followed by advanced training. Doing a Pediatric residency won't secure you work doing surgical procedures in a specialized Burn unit, but you could work as a liason with those who do.