I was having issues with the RM Blueprint package of Flash 22.214.171.124
All of my CC3 workstations have ie7 installed and flash would not work for pupils or teaching staff on any of them. Systemadmin worked just fine.
RM have today updated their 126.96.36.199 blueprint (so that it works properly with ie7) and it solved the problem for me so if anyone else is having the same problem try re-creating the package using the new blueprint.
Hope this helps someone!