If you're using the chromium-daily PPA (https://launchpad.net/~chromium-daily/+archive/ppa), Chromium will look in a bunch of folders[1] for plugins, including ~/.mozilla/plugins. I suggest you get the tarball from http://get.adobe.com/flashplayer/ and put its libflashplayer.so in ~/.mozilla/plugins. Chromium will look here for it upon startup and you're set.
If you installed using Google's deb (http://dev.chromium.org/getting-involved/dev-channel), it doesn't yet search the Mozilla plugin dirs, and thus you need to make an /opt/google/chrome/plugins dir and put the libflashplayer.so in there and it'll work.
Edit: if you're using Google's deb, you have to run google-chrome with the --enable-plugins switch. The deb adds their repo to sources.list.d, but I have no idea when they'll enable plugins by default in their repo. I'd ride the chromium-daily channel, since lots of shit is broken anyway.
[1]: http://groups.google.com/group/chromium-dev/browse_thread/th...
http://labs.adobe.com/downloads/flashplayer10.html
And if anyone's wondering why I'm not running 64-bit Firefox 3.5, it's because the Ubuntu (and possibly Debian, I've no idea) packagers still have it branded 'Shiretoko', which throws off every site searching for 'Firefox' in your UA. Hopefully by Karmic's release they'll have this sorted out.
Also, why does Mozilla not provide 64-bit builds?