This is most likely due to a signing certificate issue, especially if you do not have Windows XP SP3. The online installer is signed with a SHA256 signing certificate and older systems do not support the latest signing technologies. You can try the offline installer posted at the bottom of the Installation problems | Flash Player | Windows 7 and earlier page in the 'Still having problems' section, but there is no guarantee that it'll work.
Your best bet is to upgrade your system, if possible, to a newer supported operating system version, or install Service Pack 3, if it's not already installed, on your XP system. This page, ssl - SHA2 support for windows XP SP2 : any hotfix or dll available? - Super User, may be of assistance.