If by some chance, the version of Flash Player you are trying
to install is already present, the same one won't do anything.
To see the current version of Flash Player present in the OS,
you can use this link to Adobe to see that information:
http://www.adobe.com/software/flash/about/
If a browser is open or running while you try to install this,
be sure to close the browser in order to install it correctly.
There is a newer version 10 available, for 10.4 & later. Mine
happens to be one of the version 9 builds. Also, some of
the different players (maybe not Flash, perhaps another)
offered an Uninstaller to be rid of the older version before
replacing it with a newer one. Not sure about this one now.
You may also try 'repair disk permissions' in Disk Utility
before and after software updates, in any case, too.
There may be more to this issue...
Good luck & happy computing! 🙂