They have some Heath-Robinson-like sling on their site, but no decent cover.

I found these, made by a New Zealand company called Ecotanka. The Ecotanka bottles are pretty much identical to the Klean Kanteen ones, so these covers will fit the latter:

Tanka KOOLERS

They help to keep the contents cook, and to keep the bottle from getting scratched or dented. They also have a strap so you can carry the flask over your shoulder.

They're available in the UK as well as Down Under. Don't know whether anyone imports them into the U.S.