Sometimes, Flash is used by authors trying to protect their work. Ask for authorization first.
Any Flash site using a database or a server resource cannot be browsed offline.
By default HTTrack downloads swf files and explores them. Unfortunately HTTrack will not extract all the hyperlinks in the Flash file. The code from Macromedia will only return html files.
The best Open Source utility to explore a swf file is SWFRIP.
Open the swf file with SWFRIP.
It will create a subfolder with two files: info.txt and actions.txt.
If the file is compressed or protected, it will let you save it uncompressed.
The file actions.txt will list the URLs called by the file and show the script.
If the URLs are not obscured by functions or by an anti-decompiler utility, the links will appear in the instruction getURL("link","frame").
Add them in the scan rules:
Set options > Scan Rules
In this case, add the full path to the file names and add them in the scan rules:
Httrack will download the files and you may have to do the same with the swf files that have been fetched!
If all the links are relative, the mirror should be in working order.
The only solution is to modify the swf file with a hexadecimal editor. Ask the author for authorization first.
This method may or may not work for all the files as using ActionScript is becoming more and more common.
See Dan's site for specific Flash capture examples and more tips.