I had the same appalled reaction you all did, then I started thinking about it a bit more. Yes, it's a little narcissistic to post a picture like that, but by the same token, he has obviously put in a LOT of hard work to get that physique, so why not brag a little with a picture? That's the way his generation communicates.
And, yes, he is a member of the Queen's family (I think that's how his grandmother once described her children's position), but he's not in an official position, so he has no obligation to live up to public expectations.
It also occurred to me that if they been young people in this era, his grandparents would probably have been doing their own Instagram uploads. After all, they were pretty "edgy" for their generation.
But most important, he's an 18-year-old guy. Kids that age do all kinds of inappropriate and silly things. (A look at Princess Olympia of Greece's Instagram over the years shows a similar, um, lack of decorum.) Hopefully for him, it will interest the right girls and impress his buddies...and blow over.
Anyway, just some thoughts.