We serve something like 2.5 *billion* installer downloads per month. This is the only complaint I'm hearing about this particular issue. If the bug affected 0.01% of the population, and 10% of them reported it, we'd still see 25,000 reports.
I believe that you're experiencing the issue, but the affected cohort seems very small. My guess is that permissions on one or more files is borked (it happens occasionally, particularly on Windows).
A couple things:
If uninstalling also fails, that's a pretty solid confirmation that something low-level is wrong. The installer logs (see troubleshooting guide below) will probably tell you what's up. If it's failing to hit a specific file, I'm you'll probably see it fail when you attempt to delete that file manually. Personally, I have good luck with a little freeware utility called Unlocker in those situations, but all the caveats about making working backups and not being able to vouch for third-party software apply there.
Here's the installer troubleshooting guide:
https://helpx.adobe.com/flash-player/kb/installation-problems-flash-player-windows.html
If you're still stuck, send over the log and we'll see if we can give you some detailed advice.