I think you have to go to the desktop site while on your iPhone. From there you can copy the embed code.
Okay, I take that back. I just tried it, and it wouldn't copy the actual code. It looks like it did, but when I pasted it elsewhere, it was just the word "embed." Hmmmm.
Well you hit the share (envelope) button within the youtube player ....this will bring your email app in compose mode ..with your youtube link ...you can copy this link to wherever you want.