Jack,
That overlap spin effect is in fact called engine turning, and like your little cam, once you have done it, it is easy.
You can buy special hard rubber abrasive rods that you mount into your drill press or miller, but that is for professional use.
My friends son works for Bentley motors, which is just down the road from where I live, and he suggested going back to the hayday of the 30's and engine turn the dash on these big motors. They did, but they also anodised them black, what a fantastic finish, it makes all these carbon fibre dashes look like cheap and nasty plastic (in fact they are).
Anyway, to get back to the subject, get a piece of round wood or hard plastic the size you want the swirls and face the end up in your lathe.
Mount it into your chuck and dab a bit of abrasive on the faced end, anything will do, the harder the abrasive the rougher the swirl. I would try to begin with something like very fine grinding paste or even metal polish. Now just get a scrap bit of plate and play about, different downwards pressure, offset stagger.
When I do mine I use the miller to set the co-ords all the same to give a very symetrical pattern, and by adjusting that you can get all sorts of effects. Try to begin with setting the co-ords half the width of the rod you are using, this gives the standard fishscale pattern.
This chap does it for a living.
http://www.cs.ucr.edu/~eamonn/et/et.htm
It shows what you can do if you practise enough.
Try it jack, you've got nothing to lose, you will only gain. The only thing is that once you get the hang of it, everything in the workshop ends up engine turned.
I haven't tried it on the cat yet, he won't lay still for long enough.
John