incognitu: Flashget can use the Opera plugin with Flashget. No shell extensions though.
Reget deluxe offers rightclicks extensions under Mozilla and Firebird- it's a good manager, but not my fav.
If you want rightclick extensions for Mozilla and firebird, you must get the Flashget vbscript files (jk_link.htm and jk_all.htm, to be found at flasget folder) and transfer them to a .jar file, which is supported by Moz. Of course the tranferring is a bit tricky- I'm pretty good at java coding, but a moron when coning to visual basic. The initial scripts were made by Vladimir Romanov(Author of ReGet Pro), and are used more or less in all Windows download managers for IE integration (with small modifications, according to the program code).
It would be easier to modify the reget.jar Mozilla/Firebird extension (you will find it in the /chrome directory of Mozilla when you install reget after Mozilla) to fit Flashget. That would be a bit easier, but a bit unethical, too.