My experience of helicopter tape for this sort of thing is that surface preparation is important for making it stick (clean it with alcohol and let it dry thoroughly), but that if the area you're applying it to has too tight a curvature or a funny shape that it can't conform to it inevitably starts to peel at the edge. Then the oil gets in, and it's doomed.
Vinyl wrap of the type usually used for applying Scotchlite fares somewhat better (to remove without drama, apply heat), but I wouldn't rate its protective abilities against a bouncing chain (rather than a rubbing cable, which it seems to work for on my Brompton).
The velcro-on fabric ones the MTBers use certainly do the job, but look awful.
I wonder if low-end bar tape or hockey tape or something would take more than 5 minutes to look bad?
A bit of sheet metal is an interesting idea. Very thin stainless, maybe?
The darksider in me says enclose the chain in a PTFE tube, but the short run and large deflection near the potential anchor points (unless it's a single-speed) make that hard to do neatly. Also, even PTFE will eventually mark the paintwork, if only by polishing it.