If you are trying to download to a computer, then that should not be a problem.
Since apparently nothing happens when you click the button I can only guess that the button is not linked properly.
Instead of that page, try downloading it from the following page:
http://www.adobe.com/support/flashplayer/downloads.html
If that does work for you, I suggest you try posting in the Installing Flash Player forum where there are likely to be people more familiar with your problem. Here is a link to that forum:
http://forums.adobe.com/community/flashplayer/installing_flashplayer?v iew=discussions
