I did a bit more testing of Clones under Wine and here are my observations:
Use Wine 1.2.x for best results. I found that Wine 1.3 doesn't work well with the videos in the game and just hangs there.
Install winetricks package, and install the gdiplus component in winetricks. This dll is required for Clones to write jpg and png files (for custom avatars and level previews).
Install Clones using the standard windows installer. Upgrade to the latest version by unzipping the updated files (zip file provided in previous post) in the Clones install folder.
You should be good to go! Let me know if you've had success with this or not.