You may have to wait for the makers of Flashget 3 to update their extension to work with Firefox 4. There have been changes made during Firefox 4 development that will require some extensions to be updated to work with Firefox 4.
One thing you could try is the FlashGot extension. That one works with the Firefox 4 betas and it can be used to integrate third-party download managers with Firefox. The FlashGot home page shows that it can be used to integrate FlashGet with Firefox.