DS6 knows school comes really easy to him, but I'm not sure he knows he's gifted and certainly he has no concept of how gifted. Going to a higher grade for subject acceleration has alerted some of his classmates, but I've heard him explain it as "so I can learn new things, just like you get to do," which is sufficient for his K peers.
When DS6 was only 2, we had to talk about some of the differences between him and his playmates, as he would get very frustrated with the fact that they were "pretending" to talk like babies and would ask them repeatedly to please stop pretending and speak like a two y.o.. We used really broad strokes and talked about how everyone learns things at different ages, has different things that come easily, etc. In 3 y.o. preschool, kids would ask him to read and he'd then ask them to read to him... and wonder why they were pretending they couldn't. So, again, we had similar talks, also emphasizing what came more easily to those peers. (Drawing, shooting baskets, whatever stood out.) So I think he's noticed some of the differences for a while.
In K this year, I was volunteering once when DS left to go to math and I heard one of the kids comment to DS that he was really smart, to which DS immediately replied, "But not nearly as good at drawing monsters as you are!" All this to say, I think he has a sense of it, but just in the "we each have our strengths" sort of way, which seems very appropriate.
