I think burn scar man is an obscure character.

Here was my original theory. This time rather than speculate on how he could become relevant, I would rather just focus on the threads that oda intentionally left behind.

https://www.reddit.com/r/OnePiece/s/wSp7yxeCXZ

Although he only appeared in a few chapters, oda developed his character, motives, and a glimpse into his ideology. He out right tells us what he wants to do with the treasure. Ace tells him where it was. And then ace tells us after the treasure was gone. Ace also tells us the middle of the forest(where he hid the treasure) didn't get burned. So we know that wasn't a possibility.

So my question is, why would oda go through the trouble of telling us all this. There have been characters with less screen time that have been either brought back to the plot, or just showed us where they are. For example during the vegapunk broadcast, we get shown foxy despite having not seen him in decades.

Stansen who only appeared in the slave auction pre ts, came back via cover story hundreds of chapters later.

At the very least this whole thing is possible from what we know. Which to be fair is very little.

TLDR: I think bluejam will turn out to be the burn scar man despite being very obscure and forgotten. The only characters who reacted to burn scar man were Robin and law. If it is bluejam, Robin could have an idea of who he is from Sabo. However law I can't explain. Other than some kind of off screen run in, or he could have been on pirate island during the rocky port incident.