Hello, I am having the same problem.
When using the flash uploader, I am able to upload images just fine on my computer but my friend next to me is not able to on their computer. I turned off the flash uploader and my friend is able to upload just fine.
Using the flash uploader for them, it either pretends to upload then doesnt actually upload anything, or it will say You do not have sufficient privileges. I turned the flash uploader off and it works for them, but this is not ideal since sometimes many images need to be uploaded. I'm not sure why it's just related to my friend's computer, but I'm going to assume other users could potentially have the same problem. (I tried deactivating mod_security on .htaccess and even the whole domain just to test and there was no difference.)
Aside from figuring out what's going on, I would suggest when having the flash uploader up, also having the option to deactivate it and use the regular uploader.