Hi, I'm thinking you should use PHP sessions to pass the username around. And then use $HTTP_SESSION_VARS["name"] to get the value and pass it to flash.
Also, very simple solution to your problem, the processed data you want to pass back to PHP? the ones in hidden text fields? just put in flash - i mean either place the text fields outside of main viewable area or hide it under something, you know ...
so, either user clicks on something to submit the data for processing? or after flash movie finish playing then process data, its the same.
flash gets data from whichever source, user or DB then, process it, pass it back to PHP along with hidden preset fields.
where to pass new processed data?
instead of outputing to a HTML file(?) the new file can actually be the same flash swf(!!) or well ... just output results into a results.php file so that this new php file can get the data that you passed it via flash just now (post ot get), process the data and output the data to back to the browser.
know what i mean?
PS: I hope its helpful