Microsoft embeds Flash Player for IE/Edge in Server 2012 and ALL Flash Player updates for IE/Edge are distributed by Microsoft via Windows Updates, thus you would to need to run Windows Updates to update Flash Player for IE/Edge on Server 2012.
For all other browsers, launch that browser and navigate to https://get.adobe.com/flashplayer to download the specific Flash Player plugin for that browser (NPAPI for Firefox, PAPPI for Chromium-based browsers).
If you want to distribute Flash Payer within your organization, you would need to obtain a distribution license. See https://www.adobe.com/products/players/flash-player-distribution.html for more information. For the vast majority of uses cases, distribution licenses are free.
APSB16-37 was issued in November 2016. Flash Player is released monthly, so there have numerous releases since the Security Bulletin you're referencing was issued. For a list of all Flash Player Security Bulletins see Adobe Security Bulletins and Advisories
Finally, Flash Player isn't officially supported on any Server platform, although installation isn't prevented. For a list of supported operating systems and browsers, see Tech specs | Adobe Flash Player
Windows update is not detecting the update. Nor is it installing for once again; this download:
Microsoft Update Catalog
Which IS THE CORRECT DOWNLOAD > 2012 R2 x64 and x86.
Adobe needs to make this easier. Sure Windows embeds it but it is your product and you should be making it easy to secure it. Its insanely silly to go to Microsoft or have to deal with Microsoft for a product that is produced by your company. Find a way to fix this Adobe. It is absolutely unacceptable.
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