there's no actual player for .swf files in gentoo. they're supposed to be played by the flash-player, so install a browser and adobe-flash, then start these files from the browser.
this bug-report is about http://askubuntu.com/questions/7240/how-do-i-play-swf-files since that problem also affects gentoo. in version 1.4 of x11-misc/shared-mime-info that I have installed there is also the line an answer to above question on askubuntu suggested to change. i.e. to avoid browser telling you it can't play those files,
in /usr/share/mime/packages/freedesktop.org.xml change
didn't check if that's fixed in newer versions. if it is, consider this report as request to switch the stable version to that or to backport the fix.
This is something to be done upstream. Also, note that the current XML marks x-shockwave-flash as an alias.
Please report this to upstream -> https://bugs.freedesktop.org/enter_bug.cgi?product=shared-mime-info
And then paste here the link to let us track the issue
browsing the bugs on freedesktop it seems to be a common bug on some applications to ignore the aliases (and therefore not the fault of freedesktop). so I filed a bug on mozilla instead:
if other browsers show the same bug, please report there too...
*** This bug has been marked as a duplicate of bug 624076 ***