Re-installing from the latest Arch distribution, I had some minor issues using the standard AUR package to install the standalone Flashplayer. Most notably, it seems like the tarball from Adobe has been updated since the package last was, so the MD5 sums are off. To fix this, manually download and md5sum /tmp/packerbuild-0/flashplayer-standalone-debug/flashplayer-standalone-debug/flashplayer_11_sa_debug.i386.tar.gz and replace that with the first value of md5sums in the PKGBUILD.

If you have VLC installed, that will for some reason take precedence as the default app for running SWF files.  To fix that, add the following to ~/.local/share/applications/mimeapps.list:

[Default Applications]
application/x-shockwave-flash=flashplayer.desktop