There\'s no access to the HTTP cookies from within a Flash movie, but I now have repeatedly read that Flash Player is supposed to take care of session cookies automatically.
the question was asked 10 years ago, but I have got something to say in this regard for future readers.
The Flash Player does not transmit the default JSESSIONID in the request and cannot do it until you have set SameSite=None in the JSESSIONID cookie.
I have faced the problem where the JSESSIONID cookie is dropped in the request and I have discovered that it is because modern browsers (chrome > 80) does not allow the Flash Player to access the JSESSIONID cookie it the cookie does not have SameSite=None and Secure flash.
Please, read the announcement from Adobe here More to read about the new cookie policy: