There are 2 ways to install the Flash player under Ubuntu:
Using synaptic the following package can be installed: flashplugin-nonfree. This is a transitional package which installs the Adobe Flash Player plugin. To install this package, go to: System > Administration > Synaptic Package Manager. Click on the Search button and type in flashplugin-nonfree. Right click on the line flashplugin-nonfree and select Mark for installation. Then click on apply to install the flash plugin.
The second option to install Flash is using an add-on for Firefox called Flash-Aid. Flash-Aid can be downloaded from this site. Save the file and then open Firefox. Go to File > Open file and browse to the folder where the add-on is saved. Select the add-on and click Open. The add-on will now be installed.
Methods 1 is preferred above method 2. The flashplugin-nonfree package is standard available under Ubuntu, the Flash-Aid add-on is an easy to use tool which removes conflicting flash plugins and then installs the version according to system architecture, 32-bit or 64-bit.