Apparently its Content-type: application/x-shockwave-flash from my research although i'm still at a miss as to the content length variable since I don't understand HTTP headers all that greatly - and reading the w3 info on them isn't that useful.
So don't you have everything you need now? Just update the code I posted to point to your flash file, and change the content type from flash/swf to application/x-shockwave-flash.
(stat FLASH)[7] is the code that determines and passes on the size of your flash file. You should be all set.