I found an example and code how to copy text to clipboard with ZeroClipboard. However, it seems only to work under Firefox and does not work under Chrome/Chromium (39.0.2171.95 (64-bit)). What need to be change to get it to work under Chrome/Chromium as well?
The example you gave does not work on chrome, maybe the version of zeroclipboard is old. You can find the latest version from official website. It does work on chrome 39.0 on windows 7.