I assume you are trying to run the old site from you hard drive.
It will depend a bit on how the flash was put together but best case scenario it should just be a matter of copy the .swf files (and any other related files) to a directory on your hard disk, maintaining the original directory structure. From this directory right click the main .swf and choose 'open with' from there choose your browser (you will probably get a "blocked content" message if you are using IE, just allow the blocked content).
If this doesn't work post some more information....