Windows Server 2012 IE11 should be the same as IE11 on Win8.1... the Flash Player plugin is integrated with the browser by Microsoft.
There are troubleshooting steps for Win 8 here: http://helpx.adobe.com/flash-player/kb/flash-player-issues-windows-8.html They should also work for Server 2012.
Like I said, Mike M., don’t tell me to check whether or not the Flash plugin is enabled or not; I have done that several times with multiple Flash-Media-Rich websites and the command to enable it doesn’t show up. It makes me think it isn’t installed.
Any other advice?
Repair IE? http://support.microsoft.com/kb/318378
The thing is... Adobe collaborates with MS on the updates for IE10 &11 in Win8 &8.1 (server 2012 also AFAIK) and then hands the code off to them. It's "Redmond's baby" after that. There's a KB in Windows updates (KB2898108) that prevents downloading the ActiveX plugin throug Adobe updater from here. Even if you manually download it, it'll prevent you from installing it. I have a Win 8 and Win 8.1 test machine set up and I've tried to uninstall the KB with no success.
Unfortunately I don't have a Server 2012 machine so it limits my troubleshooting. Chris Campbell has more insight into the ins and outs of Server 2012. Hopefully he'll add to this thread.
Did you intall it? If not, go to Server Manager->Manage->Add Roles and Features-> Select there server you want to install the Feature on and under User Interfaces and Infrastructure select Desktop Experiance. After you install the feature reboot your server. After that you should be able to display flash in the browser.
You need to install Desktop experience feature to get flash work on Windows Server 2012.