I am not sure what exact Mac OS version you are using or if you are trying to install Adobe Flash on Safari, Firefox or some other browser but I will assume you have the latest Mac OS update and trying to install Flash on Safari.
Here is a step-by-step guide on how to perform a fresh Adobe Flash install on the Mac.
I do see 1 problem with the guide, the Adobe Flash offline installer link is outdated and does not work. Instead download the latest Flash player from here: http://get.adobe.com/flashplayer/otherversions/
If the Adobe site does not automatically detect your Mac OS and browser then just pick the correct options within the 2 dropdown menus.