Yes, charcoal would be safe but it won't do much. A burn is very serious. I would've place ice on the wound to stop the flesh from cooking so to speak. Every time I put ice immediately on burn or singed flesh it helps tremendously. The problem with home herbs and tinctures is that they are mild and not at all potent enough on their own to help with serious issues as these. I know from personal exp.
All is going to happen is he's going to be left with very ugly scars and it will take longer to heal without medical help. Plus infection and bacteria can set it. Charcoal is no match for hardy bacteria. I have taken microbiology before in school and I know some forms of infectious bacteria are strong and aggressive.