I installed Endnote 6 on Debian-unstable (kernel 2.7.24). It runs without a problem, integration with MS Word is perfect as far as I've tested it. Note that Endnote should be installed after MS Office. I tried it the other way around but that didn't work. Didn't have the problem of the 'empty screen' at start up where one is supposed to select the desired library. The Endnote icon doesn't appear automatically in the Gnome menubar (I'm using either Gnome as desktop manager, or Fluxbox without icons) but can be found in CrossOver's Windows/Icons directory. For the startup command see earlier mail above.
As reported for Endnote 7, I too get the flickering windows occasionally, but it's not a big worry.