Private messages cause the default chat tab to flash, however no such functionality exists for custom chat tabs.
For people that have a separate chat tab for Guild-related messages, but still keep their tabs docked to the normal chat window, this addon will cause the Guild chat tab to flash when receiving a guild message and the Guild tab is not the currently active tab.
Caveats: The guild chat tab will need to be named "Guild" for this addon to work.
Currently only Guild messages and Guild Achievement messages cause a flash.