Firefox lets you disable these features through its advanced properties. Enter
about:configinto the address bar of Firefox, accept the "I'll be careful, I promise!" warning. Then enter one of the following in the
Searchfield at the top:
browser.download.manager.flashCount- set to 0 (zero) to disable blinking in windows taskbar.
browser.download.manager.showWhenStarting- set to false to prevent the download window from showing at all (it won't open if it's not already open) when you start a download.
browser.download.manager.focusWhenStarting- set to false to keep the download window from stealing focus/showing when a download starts.
Almost directly copied from http://superuser.com/questions/63762/is-there-way-to-disable-download-bar-blinking-in-firefox, thanks to Adam Ryan. :)