To install flash in Ubuntu use:

sudo apt-get install flashplugin-nonfree

This works on Ubuntu 32bit and 64bit. Flash is slightly unreliable on 64bit Ubuntu, but it works nonetheless.

You can also install two open source versions of flash that have limited to good support.

Gnash supports most older versions of swf animations, and newer versions should work better as updates are rolled out. Install gnash with:

sudo apt-get install gnash

You can also try swfdec:

sudo apt-get install swfdec