PrintMonitor (the Notification Manager) will flash an Icon when an error occurs or as a signal when to feed paper manually, if you have configured PrintMonitor via its Preferences to do so.
When PrintMonitor signals you, typically you'd open PrintMonitor and perform the directions given in the dialog or note any error state it alerts you to. By addressing the situation this should stop the flashing icon until you print again.
Check your PrintMonitor Preferences to see what you have set by launching PrintMonitor, then selecting Preferences in the File menu. The likely reason why the PrintMonitor icon flashes is due to your settings.