I'm not too familiar (aka haven't hear of:P) carbon-fiber and kevlar, and aluminum (I have over 10 lbs) is light, cheap, strong (for its weight), knife-resistant, easy to work with and most importantly
SHINY
Sorry, but I am absolutely obsessed with aluminum. Kevlar and carbon-fiber sound good (I assume you're familiar with them). If you're serious about trying to make chainmail, you can find a guide to making it at
http://www.chainmailman.com/tutorial.html. I'm not too sure what non-metal chainmail would be like... Are kevlar and carbon-fiber rubbery or hard?
You may want to take a look at my chaimail link at my website (
http://www.altay.vilko.net/), though currently it just has links to other chainmail pages.
About the idea of a chainmail-pouched sling, the hardest parts would be making the chainmail just the right size and hooking it to the sling. The easiest way to do this would probably be to make the chainmail pouch first, then braid the regular (
http://www.slinging.org/20.html) pouch around/through the loops until you braided the entire pouch onto the sling.