Bliss sells a travel flat iron, but it has to be plugged in. It's the Metropolis Technology Tourmaline Ionic Travel Iron. No doubt you could probably find it cheaper from someplace else. Blis usually has a pretty huge markup, IME.
I agree that they probably need more power than batteries can provide.
I did have a rechargable curling iron back in the 80's though... so it might be possible. There also were some propane powered curling irons I remember from back then. Sounded dangerous -- especially when you add hairspray to the equation!
Suddenly when we talk about a technology related to hair care while on the road we go OT.

Kidding aside, I'd think this has at least as much and possibly more relevance in the womens' forum as it does here... and it's likely to get more responses there.