I use Debian. In Debian, the easiest way to deal with flash is to add www.debian-multimedia.org to the sources.list, and then just apt-get install flashplayer-mozilla.
Xubuntu is Debian-based and it's even easier. Open up Synaptic package manager, click the box on [whatever the package was named], select "Install" then click on "Apply" and "Yes", and wait for it to download and install. It even fetched the very latest from Adobe.
HOWEVER, it doesn't always work. I found one thread where somebody uninstalled a number of related drives, reinstalled in a different order (not clearly stated), and he said it worked. Order is apparently important.