Dunno about Windows XP, but I suspect older versions of Windows are having the same problems with the Adobe updates that older versions of the Mac OS are having, in that the default updater doesn't work.
You do need to update to the very latest version of Flash (which is probably where the update needs to be applied) because there are a number of very deadly attacks being exploited in the wild. To achieve that update, you might have to do some digging around on the Adobe web site. On my Mac, I discovered that if you follow the trail of links from the failed update to trouble shooting on the Adobe site, eventually you get to alternate ways to update, one of which will eventually work. I know, pain in the keister, but from what I hear, you need to get it to work somehow lest you find your entire computer and all the data on it compromised beyond usefulness. The bad guys are evidently having a field day.
Oh, yeah, and rumor has it that the malware has so far only been found in the wild for Windows. But of course, it's coming for Macs, too. EVERYBODY needs to attend to this one.