Which "cloud" did you get?
Adobe Creative Cloud.
That's odd. I haven't seen anything to install CC with Flash Player. AFAIK, you have to sign up for CC to get it. I have Creative Suites 3, 4, 5 & 6 and I'm not ready to use the Cloud, so I haven't signed up for ANY of it. CS6 now uses the Creative Cloud updater to install CS6 updates, but that's as close as it gets. There is no connection I'm aware of between the CC and the free apps like Reader & Flash Player.
If you have any Paid apps like Photoshop, Dreamweaver, Encore and the like, then your AAM (Adobe Application Manager) will have upgraded to the CC updater. If not, use the Creative Cloud Cleaner to remove it: http://helpx.adobe.com/creative-suite/kb/cs5-cleaner-tool-installation-problems.html
and install Flash Player using the appropriate link below:
Thanks Mike !