I recently had a total computer failure and had to buy a new one. In the process I have lost Flash Builder 4.5. I have the latest Creative cloud subscription, but Flash Builder 4.5 is not included in the "previous versions" section of apps to install (and 4.5 is the only version that will complete a build of a very old program we are still using).
I have found our old CS5.5 Web Premium installer and installed 4.5 again, but I have no serial number records from back then so I am forced to use it as a trial version for now.
I cannot find anyway to retrieve the serial number for this reinstall, nor activate it using creative cloud.
It's not exactly what you're asking for, but you can get the v4.6 download here: Adobe - Adobe Flash Builder 4 : For Windows : Flash Builder 4.6 - Windows
I recently had a similar issue trying to run older versions of Flash Builder. The answer I was ultimately able to get was that Creative Cloud offers v4.7 only, and CC will not entitle you to get a serial number to activate 4.6 or lower. Your best bet would be if you still have the purchaser information from when you bought your old license.
I'm suspicious of how actively this forum is monitored, considering your last post doesn't have a response either. I was able to get attention by asking on Twitter (yes, it does have a use!). If the web chat "registration" category doesn't give you a good response, try tweeting @AdobeFlashCC or @AdobeCare