How can we reduce the size of heavy flash files

I guess that your audio content is in high quality and/or you have used bitmap images in your animation. For audio, you may consider to tune down the quality to achieve a smaller file size. Audio editors like Audacity should help. For images, you better consider using JPG with lowest acceptable quality. Most image editors allow you to select image quality when saving as JPG. Hope this helps. Finally, if you don't need to play the animation on the internet, but to let others to download and watch themselves, you can simply ignore my previous suggestion, and to use a Zip utility to zip it.

You can use KbG archiver compression software or rar software to compress the file.

The only way I could think of to do it is to compress the file like crazy(kind of like the process the recycling bin uses), and then zip it with something like winzip, winrar, etc. They're all free to use. I dunno if this will really help, though.

There is no chance to reduce swf file.. You need to have the project file , then we can realize what to do... ( reducing sounds or reducing frames...) Perhaps this project isn't good made to produce small swf file...