I've tried the physics approach before using a physics rope
as a base. I didn't quite get it to have the feel of a cape. I probably didn't tweak it enough though. If you lower the density of the pieces of rope and reduce the gravity it can look close to what you want.
The only thing that's lacking is for it to catch wind. If the cape were in a complete vacuum it would probably act just like the rope. To do air resistance it might be enough to apply a force 100*sin(anglediff(link angle, angle of motion)) perpendicular to each piece of rope. I haven't tested that but it should simulate more resistance when the rope moves perpendicular to it's angle, and allow free motion when moving the same direction as it's angle.
This is all a rough idea but hopefully give you some starting points of how to tackle it.