Good method:
Flash should not have any actions with server sessions (it`s a bad style). Before you show any page (mask it as preloading) you must ask your server for some data. Server already know users and its sessions and must return you the data or an message, probably like this: "user don't have session yet, do login". But it's work only if you have an influence on a server side developers.
Bad method:
You can remember any user data in a SharedObject it`s store data on a user's computer, so it will be accessible between a browser refreshes (but to do this you need some programming skills). It's bad because of security reasons – storing and sending sessions not safe.
SharedObject Documentation
P.S. And please, forget about hiding something in a hidden text fields :) use variables.