I've been having this issue since I got windows 8 and now I'm in 10. I've had to manually install whatever is the closest to the current version and even then Flash is always crashing. I think this is a serious issue that needs to be addressed with Windows users upgrading to Windows 8 and 8.1 and even testers like me who have 10. If this isn't fixed now, I can imagine the problem growing in the coming months to where it takes several updates to fix.
I've just tried with https://aihdownload.adobe.com/bin/live/install_flashplayer16x32_mssd_aaa_aih.exe
file version 220.127.116.11 on Windws 8.1 and suprise suprise the same behaviour.
I downloaded and ran in firefox and it elevated, deleted it's exe and sent me to the url above. Manually double-clicking the file in Windows explorer it just shows the empty box and doesn't remove itself or show the url, if I 'run as Administrator' to execute it will again delete itself and show the url! Either way I have to use task manager to terminate the process as the exit buttons are unresponsive.
Looks like this is a popular issue on Installing Flash Player forums but so far I can't find a useful reply!
You have to by-pass the buggy downloader exe and download the full installer. See
Re: Unable to install flash player. After downloading the Adobe FLash Player Installer and running it, a grey pop up window opens up but nothing is displayed in it. There is no progress bar or anything.
Unfortunately full installer do not provide automatic background update. I'm seeing this blank installer screen for almost half an year on diferent PC's with different OS'es. It's absurd that Adobe FlashPlayer team can't resolve this for this long. As I see they don't care. I'm waiting this Flash thing to be dead soon. This buggy thing was annoying and swallowing our resources for too long. Congrats to FlashPlayer team. Go look for a job.