I'm assuming this is the online installer downloaded from one of the get.adobe.com/flashplayer pages. The online installer isn't supported on OS X 10.6, but there's a bug on one of the pages and it's delivering the online installer instead of the offline installer. This bug is due to be fixed soon.
In the mean time, please use the offline installer posted at the bottom of the Installation problems | Flash Player | Mac page, in the 'Still having problems' section.
I tried using the installer posted at the bottom of the installation
problems | Flash Player | Mac page in the 'Still having problems" section
and got the same greyed out install box at the bottom of the installer
Just click on check box near to "I have read and agree to the terms of the Flash Player License Agreement". The "INSTALL" button will get enable.
SO SIMPLE! YOU HAVE MADE MY DAY!