I can't help you with why the auto-update's not working for you, but I can point you in the direction of the full installers:
- Windows: https://helpx.adobe.com/flash-player/kb/installation-problems-flash-player-windows.html
- Mac: https://helpx.adobe.com/flash-player/kb/installation-problems-flash-player-mac.html
Same instructions for both pages: scroll to bottom of the page - you can download the current, full installers from the section headed "Still having problems?".
Alternatively, if you need to download the full installers for distribution around an office, you should apply for a distribution license from Adobe. It sounds like an ordeal, but it's just a quick web form, costs nothing, and lasts 12 months. They'll send you a unique URL which replaces the old distribution page. They even send you a reminder to renew your license.
What a stupid decision to remove the offline installer, the Auto Installer always failed for me too, just constantly hung at 0% when it came to downloading updates and like the original post the only way I could install Flash updates for the last few years was by using the offline installer, which somebody has now decided to remove.
I've had no option but to apply for the distribution license, which seems to be a bit overkill as I don't have any intention to redistribute it, I just need one personal update to use on one domestic home use PC, but hey!, that is adobe's decision and not mine. It just doesn't seem to make much sense to me, to have staff now manually viewing and approving personal use download applications via the redistribution form, where a link did the same thing, with no manual labor involvement from staff.
Hopefully my application will be approved, or I will have no other way to download flash player updates. A quick google search shows many others with exactly the same problem.
What OS and browser are you using? You could even opt for "Allow Adobe to Install updates" to install the Flash Player updates in the background.
Distribution licenses are for enterprise customers to distribute Flash Player within their organization. They are not for individual users. If you read post #2 you'll see the offline installers didn't go away. We do have a help page that has a link to the full offline installer.
If you provide information on the issues you encounter while using the online installer I'm more than happy to assist with troubleshooting the issue with you.