I think I understand. You want to process information from a
SWF to the database using
PHP WITHOUT refreshing the current page. I'm no guru, but you're limiting the options and hoping for more capability that Flash or any web page has to offer.
You can process the information using a secondard
PHP page. Have Flash send a request to a new window (_blank) with the information you want to pass. That should be simple. The problem you'll run into is Flash CANNOT do anything with the processing. The page is required to do the processing first and forward it to Flash. If you don't want to refresh the page, then you can't update Flash. Using GET and POST, and FLASHVARS are the only three methods Flash has to receive (send) information. If you don't use then you're come up short.
If you are worried about losing the information the user has selected, have Flash send the information to
PHP and store it in a cookie. This way it can be retrieved, process and returned to Flash on a refresh. Sorry I could help ya more.