I had this issue too when I recorded something using Jing and it turned it into SWF which is a flash file. Flip4Mac may work, but what I ended up doing was this. I opened the flash file using a browser (in my case Safari). Then I used Screen Flow or SnapZpro to record what I was watching in Safari.
The reason I had to even do this was because I recorded something in Windows using Jing (it was free and had nothing that supported windows) and then I put that on my Mac and used a "purchased" recording app that I had to convert that SWF file into a Quicktime file.
Sounds crazy, but it worked and I hope this helped.
Thanks for the feedback, but I'm not sure if I'm saying it right. The problem is that I'm using a CMS (Weebly) that requires me to upload a video file that is a SWF format. It will only play SWF. I have AVI and FLV files and and am unable to convert it to SWF. I know this may sound a bit weird, but that's what it asks for.