New to Linux and using 14.03 Gnome Shell
 

How do I replace Adobe Flash Plaayer

I don't really understand your question. What would you like to replace it with? Do you want something with the same functionality or do you have a damaged version and want to replace it with a non-damaged version?
The flash player has nothing to do with gnome. It works with any desktop.
jdk

Are you having trouble with it working on a particular browser? It's likely whatever problem your having has nothing to do with flashplugin. For example, if you're running chromium with the "HTTPS Everywhere" extension running, flash will crash every time. That's just one example. Now if you install Google Chrome, it comes pre-packed with it's own version of flash; you never need to think about it.