The Kiln Client itself is currently Windows-only, but the extensions are cross-platform, including KilnAuth. To get them, go to Resources/Kiln Client and Tools:

When you get to that page, look at the second section, labeled "Mercurial Extensions". Click the download link, and extract the zip somewhere. (I keep all of my Mercurial extensions in ~/hgext.) Then, enable KilnAuth by adding the following to your ~/.hgrc (~\Mercurial.ini on windows) file:
[extensions]
kilnauth=/path/to/kilnauth.py
Once you have that set up, you can remove the password section under [auth]. Mercurial will ask you for your password once, and then the tokens that Kiln uses will be saved and you shouldn't have to type it again.
Thanks to Anton for the screenshot.