Basically you can install flash player on a 32 bit ubuntu machine by using apt
$ sudo apt-get install flashplugin-nonfree
It downloads and installs flash player. And all you have got to do in restart firefox.
The issue I faced was how to install flash player on a 64 bit ubuntu machine. As far as i am aware there is no stable release of any flash player for a 64 bit machine. The only way to make the flash based websites work is to install something known as "nspluginwrapper".
nspluginwrapper allows you to use 32 bit netscape compatible plugins on x86_64 browsers. So, the flash plugin is 32 bit but nspluginwrapper allows it to run on browsers compiled for x86_64 machines.
To install flash plugin for 64 bit browser using apt:
$ sudo apt-get install nspluginwrapper flashplugin-nonfree lib32mss-mdns
Restart firefox and bingo, you have flash plugin on your browser.