After some stumbling around in fustration trying to find a way to run swf locally, I found a Ubuntu thread that had a solution that worked and would like to share here.
I'm using Linux Mint 17 64bit ftw.
1. Edit /usr/share/mime/packages/freedesktop.org.xml (e.g. sudo gedit /usr/share/mime/packages/freedesktop.org.xml)
2. In freedesktop.org.xml find "<mime-type type="application/vnd.adobe.flash.movie">" and change it to "<mime-type type="application/x-shockwave-flash">".
3. Run "sudo update-mime-database /usr/share/mime"
Optionally install/reinstall the flash plugin. Personally though I had the adobe-plugin installed already when I did the above and when I logged out of my admin and into my daily account I was able to run a swf in Firefox.
Source: http://ubuntuforums.org/showthread.php?t=2218732&page=2 (Post 13) (which sources https://bbs.archlinux.org/viewtopic.php?id=173295&p=2)