I saw some guides to download Kongregate games from the archive, wich use external programs to do the job like Live HTTP Headers Add-On, Sothink SWF Catcher, UnPlug add-on for Firefox or sites like FILE2HD.com.
I want to show you the basic on "how to" without all of this.
Here we go, let's get a Kongregate game example :
http://www.kongregate.com/games/krangGAMES/beloved
1) Well, load the internet page and in your browser write view-source: just before the link.
In our example this would be :
It can be written without :http// it will be automatically put in as always happens with sites.
2) You'll see the source code of the page, press ctrl+f and search for "swfobject.embedSWF".
Different results will show, browse till you get the one wich has the title.swf of your game into, in this case :
3) Copy-paste the link in another tab of your browser, you will open the full window page game.http://chat.kongregate.com/gamez/0014/1416/live/Beloved.swf?kongregate_game_version=13334592
Now you just have to do a "save page as" and the process is done.
Have fun!