No, XLink Kai can't be used on a Chromebook because it's running on Chromium while the software is compatible only with the Windows operating system. You'll have the possibility to run XLink Kai on the Chromebook after the developers release the product for this operating system.
Visit the official website and let the developers know that are users who need the software on Chromebook, but don't expect that it will be released. Some technical difficulties and requirements might come into play and could affect the release.