I just use a tea-towel and some Windex on my chrome X-Pole, so I’m not much help!
But I googled to see what Chamois was, and apparantly it’s just the leather from the Chamois animal (which is like a mountain sheep).
My only concern would be the oils that would be in it due to the whole tanning process. Unless it is synthetic, then I wouldn’t worry about it. It won’t scratch your pole. It says it’s non-abrasive.
Just FYI, this is what I found on Wikipedia http://en.wikipedia.org/wiki/Chamois_leather
I think it sounds like a great cloth the wipe your pole with. How much did you pay for it at Canadian Tire?