Judging from this example found on adobe.com, it does appear that flash supports POST:
The following ActionScript uses POST to send variables in the HTTP header. Make sure you test your documents in a browser window, because otherwise your variables are sent using GET:
var firstName:String = "Gus";
var lastName:String = "Richardson";
var age:Number = 92;
getURL("http://www.adobe.com", "_blank", "POST");
Does this mean that I can pass an unlimited number of variables, since they're not appended to the URL?
I'm still very new to this, as you can tell. Thanks a lot for all help!