C# – What’s the best ASP.NET file type for a (non-SOAP, non-WSDL) web services project

Others may disagree, but I actually don't see a huge problem with handling it the way you are now; that's probably how I'd handle myself, at least initially. One way or another, even down the road, you'll probably want to keep the Flex app aware of the authentication state of the session, so if that means checking the ASP.NET session token directly, or some other cookie you set when you set that one, it seems like a fine and reliable way to go.

I do see what you mean about the services redirecting, but even so, with forms auth, it's not so much the service specifically that's handling the redirecting so much as the ASP.NET app itself. Later, should you need to use a different authentication scheme, you can consider that scheme's specific implementation considerations. Unless you've got concerns about using forms auth in general, there's probably no need complicate your approach simply because of the Flex client and Web services.

You should not use ASMX web services for new development. Use WCF instead.

In your particular case, see ADO.NET Data Services (renamed to WCF Data Services in .NET 4.0).