There are no inherent problems with Macs/Safari/Flash. Working on a Windows machine and not working on a mac has no significance: naturally Flash Player for Windows is a different piece of software from Flash player for OSX.
You're in an iPad forum, by the way.
Open System Preferences > Flash Player then select the Advanced tab.
To make sure the latest version of Flash is installed, click Check Now under Updates.
You can access Sysem Preferences by clicking the Apple menu icon top left in your screen.
Or by going to HD > Applications > System Preferences
* You posted in the correct forum.
This not the iPad forum.
You styill haven't told us what Mac you have and what version of OS X and Safari, but:
You can check here: http://www.adobe.com/products/flash/about/ to see which version you should install for your Mac and OS.
You should first uninstall any previous version of Flash Player, using the uninstaller from here (make sure you use the correct one!):
and also that you follow the instructions closely, such as closing ALL applications first before installing. You must also carry out a permission repair after installing anything from Adobe.