запрос файла с использованием куков

[unodj]

Скорее всего вы правы.
Хотя явного запрещения отправки заголовка Cookie я не нашел

The following request headers cannot be used, and the restricted terms are not case-sensitive (for example, Get, get, and GET are all not allowed):

Accept-Charset, Accept-Encoding, Accept-Ranges, Age, Allow, Allowed, Connection, Content-Length, Content-Location, Content-Range, Date, Delete, ETag, Expect, Get, Host, Keep-Alive, Last-Modified, Location, Max-Forwards, Options, Post, Proxy-Authenticate, Proxy-Authorization, Public, Put, Range, Referer, Retry-After, Server, TE, Trace, Trailer, Transfer-Encoding, Upgrade, URI, User-Agent, Vary, Via, Warning, WWW-Authenticate, x-flash-version.

Поиск "cookie" по хелпу flash показывает только разделы, связанные с SharedObject