Is it possible, using a registry hack or some other method, to supress the taskbar "flashing" when someone sends me an instant message?
This is a registry specific feature.
When a window is opened it will either appear over an existing window or it will appear minimised on the toolbar and flash when it’s available to use. This Registry alteration will enable you to control this behaviour. It’s ideal for dealing with pop-up windows, and will enable you to keep them on the Taskbar rather than having them obscure whatever you’re looking at.
There are two settings to adjust depending on which way you want new windows to appear.
The first controls the way in which a new window appears. Go along to HKEY_CURRENT_USER \ Control Panel \ Desktop and create a DWORD value called ForegroundLockTimeout, or modify the existing one. The value that you give it will determine the amount of time the new window appears over the old one. Enter a value of 0 and the new window will go over the top immediately. Enter the default value of 200000 (0x00030d40 hex) and the new window will appear on top for 200,000 milliseconds and then minimise to the Taskbar where it will flash.
This flashing is controlled by the next tweak which will set the number of flashes. Create or modify the DWORD value ForegroundFlashCount and set a value for the number of flashes you require. 0 will make it flash infinitely or you can go for the default value of 3. Select 1 flash and it will appear and just turn orange immidiately.
The below might not be the solution (as Wil points out), but in that case we have to resort to 3rd party addons.
You should check out Messenger:Mate for Windows Live Messenger
Try turning off the notification.
Go to your settings and then to the Alerts and Sounds part.
Tick off the boxes for the messages you don't want. In your case, "Display alerts when a message is received"