My personal favorite theory is the cabbage merchant's descendant, but I honestly think he's just someone new.
However, I do have a crack theory to throw out there. Maybe Amon is Zuko. Think about it, his family was destroyed by a firebender( Ozai was a firebender and was responsible for Zuko's mother killing his grandfather, Azula being Azula, and Iroh loosing the throne.) Zuko's face was severely burned by that same firebender, and there is a history of mental instability in the family line.
Even better, Zuko is still alive but no longer the firelord, so he has free reign of where he goes. His face is high profile, and honestly how could forget it, so he uses the mask to hide it while still technically telling the truth with the burn excuse.
Except that Zuko is even older than Katara, and he'd just be a wrinkly old man.
Amon is obviously a healthy adult
Hence why it's a crack theory. The point was to join in on the fun of crack pot theories that obviously are wrong.