Thanks for reporting the issue. We will try to reproduce it at our end and get back to you with a solution.
Update: Same issue with updated versions since 126.96.36.199 all the way to latest 188.8.131.52.
Update: issue continues to version 24.0.0.x. No response. Adobe has stated the following
"While the customer might have been able to “install” Flash Player with previous
installers, the installer was not registering the player and was silently
The underlying issue here is that our ActiveX installers can not be run on Windows
8+ or on Server 2012+, only Microsoft can install Flash Player on those
systems. While we might be able to install the binaries, we do not have
permission to unlock and properly register Flash Player for usage, only
Microsoft can do this. We can not support this install scenario and the
customer must go to Microsoft to petition an installer if they are unable to
leverage the player that comes with the “desktop experience” package. "
This has been happening much longer and does not seem to fit the issue I have been dealing with.
You are quoting a comment I made on a different topic, completely unrelated to your issue. The OP of that topic was attempting to install Flash Player ActiveX on an OS version that Microsoft embeds Flash Player ActiveX Control in, and thus, the standalone installers (EXE or MSI) do not install Flash Player ActiveX Control on those systems.
I currently do not have access to a Server 2003 system to attempt to reproduce the error.
We can attempt to troubleshoot by viewing the install log files. Please provide the FlashInstall.log file saved in C:\Windows\System32\Macromed\Flash AND C:\Windows\SysWOW64\Macromed\Flash. Upload both files to cloud.acrobat.com/send using the instructions at How to share a document and post the link to the uploaded files in your reply.
If you are using the MSI installer, also provide a MSI.log file with v+x (verbose and extra debugging options) enabled.
Note that Flash Player is not officially supported on any Server platform. The error you are seeing may (or may not) be as a result of that. The log file may provide additional information for debugging.
 this means we don't develop for it, nor test on it. See Tech specs | Adobe Flash Player for supported platforms and browsers.