Notification of Flash player version updates

Question

Looking for an auto-notification means by which we can be prompted of pending Flash Player update releases so we can package the new version for distribution of our users ahead of time.

Answer 1

This is actually pretty easy, and we provide pre-packaged bundles of the ActiveX and NPAPI versions of Flash Player ready for distribution through AD/SCUP/SCPD/etc. 
We also provide an Extended Support Release, which is still patched with security fixes and released in parallel with our generally available release, but the intent is to insulate organizations from the risks associated with new feature development, while keeping the up-to-date from a security perspective.  For organizations that have strict testing requirements for feature-bearing product updates, this is our way of providing pain relief as browser release cadences and the security landscape have necessitated a much faster cadence for Flash.
First things first, you need to apply for a Flash Player distribution agreement.  It's free.  The license for the individual download doesn't technically grant you permission to repackage and redistribute the player, plus you don't get access to all of the prepared packages and notices.
We expect some changes on the distribution side of the house to increase the number of applications coming in soon, so if you're redistributing Flash Player inside your organization now and you don't have a current distribution agreement, take a few minutes to fill out a fresh agreement before we get absolutely crushed with new requests and our processing time takes a hit.
Adobe Flash Player Distribution | Adobe
Once you've been approved, which should hopefully be pretty quick, you'll get access to our distribution portal, and I believe you'll get automatic notifications by virtue of being on the distribution list.
You should probably also sign up for the Adobe Security Notification Service, just so you're sure to be notified of critical updates to any of our products that may be on your network:
Adobe - Security Notification Service
Here's the system administrator's guide for Flash Player, which probably has some stuff you'll find useful:
Adobe Flash Player Administration Guide for Flash Player 14 | Adobe Developer Connection
Flash Player releases on a monthly cadence, aligned to Microsoft Patch Tuesday, in addition to occasional out-of-cycle releases, when we need to address critical security issues.
Flash Player also includes an automatic update service, which we highly recommend that you take advantage of, particularly if you're already really busy.  If you're updating on an ad-hoc basis, you're leaving your users exposed to threats that we've already mitigated.  Given the level of sophistication we're seeing with both organized crime and nation-state sponsored hacking, it doesn't take long to do a binary diff of a new version and reverse-engineer the fixes for use against older versions.
While we work closely with our partners in the security and research communities, and the vast majority of those updates are the results of issues that are discovered and disclosed responsibly, it's important to keep your clients updated, especially when we're issuing out-of-cycle patches when an active exploit has been identified in the field.
Anyway, I think the resources above will keep you informed of anything critical and give you access to all of the tools necessary to distribute Flash Player inside your organization, while minimizing the associated work.
Good luck!