First off, we’ve never seen Killer’s full face before which could indicate that he’s hiding something. As a child he had his eyes covered and as Kamazo he had his forehead covered like Pudding does.
You could say that him covering his face is just part of his design but when he was Kamazo there wasn’t really any reason for Oda to keep his forehead covered when we’ve pretty much seen his whole face. Also, when he fought Zoro you can see the lines under his forehead which usually only appear under people’s eyes.
Even when they are on the forehead, they cover the whole thing and not just the middle like Luffy’s face here.
To back this up even more, the lines under Pudding’s forehead only cover her eye area, similar to Killer’s.
It’s very much possible that the three-eyed people are wanted by the World Government just like the Oharan scholars are, as they posses the power to read Poneglyphs, hence why Killer would need to cover his face in order to hide from them. This would explain why he wears a mask.
Another interesting point about Killer’s design, is his Jolly Roger.
You see that it has 3 stripes, 2 of them cross the Jolly Roger’s eyes, meaning that this could be a hint to his 3rd eye. His helmet also has 3 stripes.
Reasoning behind Killer’s 3 Eyes
You might be wondering why Oda would make a minor character like Killer have such a rare and powerful ability. Well there’s a few reasons for this. Firstly, Kid is meant to be a direct rival to Luffy and his dream is also the same as Luffy’s so it would make 100% sense if he also had someone who could read Poneglyphs as his crewmember.
Also, it wouldn’t make any sense for him to go after a copy of Big Mom’s Poneglyph (assuming that’s what he took) if he never had someone who could read it.
*Theory by Return of Gin