As user (non-admin) with Citrix, there can be a problem to show internet websites with flash objects on it, but as an Administrator, you don't have any problems. To fix this problem you need to change some rights in the Windows registry.

"Change the permissions to "READ" for everyone on the two registry keys below. (Ensure it is replicated to the child objects.)

HKEY_CLASSES_ROOT\TypeLib{D27CDB6B-AE6D-11CF-96B8-444553540000}
HKEY_CLASSES_ROOT\CLSID{D27CDB6B-AE6D-11CF-96B8-444553540000}

Next time the users login, it works.
By default, EVERYONE is denied. Hence the error."

Source: Citrix Forums

Warning Serious problems might occur if you modify the registry incorrectly by using Registry Editor or by using another method. These problems might require that you reinstall the operating system. Microsoft cannot guarantee that these problems can be solved. Modify the registry at your own risk.

If you want information how to backup your registry, see MS KB 322756.