If you're using ASP.NET then you're better off using a .NET product for Flash integration. Fluorine and WebOrb are two options. We've used Fluorine for years and are very happy with it.
Flash Remoting is a technology Flash/Flex can use to communicate with a back end. It uses HTTP to transmit messages and encodes individual messages in AMF, a binary protocol that is extremely efficient to encode/decode in Flash.
Another option is RTMP which was originally designed for video but is also used for data. It internally uses AMF for encoding individual data packets. RTMP utilizes a constant connection and enables two-way communications. It generally requires a separate port for communications but some products, including FMS, support HTTP tunneling which will send RTMP connections over port 80. I'm not sure if Fluorine or WebOrb support HTTP tunneling.