Last time I had some huge problem on site with ssl security and SWFUpload and other flash uploaders. There was always error #2038. Additionally there was a problem with sharing content from https site on Facebook. I have spent a lot of hours to find the solution and I found it! There was problem with ssl certificates.
First of all you will need original and not self generated certificates if you have same issue because Flash has problems with second ones. The site server is on Nginx so you will install certificates properly here is the instruction. And the main point is Concatenate the primary certificate and intermediate certificate. If you won’t do it yours page will be working properly but not the flash uploader and even when you try to
curl https://your-site.com
you might see error that explains that there is problem with certificate.
What is interesting that on Windows and Mac Os machines the flash works properly even without concatenating certificates and there is problem on Ubuntu. But on every system is problem with sharing on Facebook as it depends on FB servers configuration.