You should only have to apply for the End-User Redistribution License *once*; after that, Adobe should be emailing you a notification with the link to the download URL covered by that license each time a subsequent Flash Player release is published.
But there is another option: You can configure and synchronize Adobe's Flash catalog, direct to Patch Manager, which does have a direct download link. But BEWARE! Their Flash catalog is notoriously problematic. Because they use generic naming on their installer files, only the *CURRENT* package in that catalog can actually be used. If you try to publish an older package, you'll get the wrong binary.
The catalog can be found at http://fpdownload.adobe.com/get/flashplayer/current/licensing/win/AdobeFlashPlayerCatalog.cab.
Navigate to the Software Publishing node, right-click and select Synchronization Settings.
Select the "Other Catalogs" tab, click on "Add Catalog".
Paste the URL of the catalog into the "Catalog Path" textbox, and complete Publisher, Name, and Description to suit your needs.
Synchronize the catalog to get the Table of Contents, then go to the "Subscription" tab, and enable the product(s) you want.
There is only one: "Adobe Flash Player".
Also.. just like their Reader and Acrobat catalogs, sometimes their packages just don't work (so definitely keep ours around as a working alternative) :-)