Where are you downloading Flash Player from? and which version?
Could you go to http://get.adobe.com/flashplayer/otherversions/ and download a Flash Player 11 for your computer, and let us know if you still face the same problem.
Moving this discussion to the Installing Flash Player forum.
Try to download and run the installer from http://helpx.adobe.com/content/help/en/flash-player/kb/installation-problems-flash-player- windows.html#main-pars_header
If that still fails, you may need to update your Windows XP to SP3.