Brian Kiel what version of the Adobe Application Manager are you using? You can locate the application in Applications/Utilities/Adobe Applicaton Manager/core. You can find the version by selecting the Adobe Application Manager and selecting Get Info from the File Menu.
Also you can download and install the released trials and choose the option to license this software once installed. You will then want to enter the Adobe ID tied to your Creative Cloud subscription.
Currently running Application Manager 184.108.40.206 (was the one that Adobe gave me when I signed up for CS6 cloud)
As for downloading trials & then licensing them after-the-fact... That was what I just finished trying, and it seemed to have worked. FlashPro is installed (& automatically linked its license to my cloud subscription). I guess I can install the other problem apps this way as well... but it just seems odd to have to do it this way when Adobe has actually created an Application Manager that should do this all for me.
Oh well. Problem resolved. (although in more of a workaround manner)
Thanks for you response.
And it seems that, after I installed FlashPro via the trial, I'm now able to use the Application Manager to install Photoshop, Illustrator, etc. (Like the Flash trial added/fixed files that were causing install problems for the other core CS6 apps)
tl;dr: Had problem with Application Manager installing Flash, Photoshop or Illustrator... installed Flash as trial, now Photoshop & Illustrator can install from the Application Manager.