Is there a method (or tool) to convert video from a SWF container to another more portable format (e.g., H.264) I have a client who has misplaced the original source video, only has an SWF, and would like to use it in a non-flash environment. 

Is there any way to do this?

So far, I've tried ffmpeg but it's failed, complaining about the compressed SWF.

[swf @ 0x101807c00] Compressed SWF format not supported

Any help would be appreciated.
You should get a SWF decompiler (perhaps one of the trails for: Sothink SWF Decompiler   or Decompiler SWF) and use that to find the nested movie file, and extract that.