You do need a Flash Media Server (or an open-source alternative such as Red5) to be able to stream video from the client to the server, which is essentially what you want to do here. There is no way to do that using HTTP POST.
You can, however, draw your Video display object to a bitmap each frame, and upload those bitmaps on the fly using regular HTTP file uploads. Although as you can imagine, that's not exactly ideal from a performance point of view. You'll also bump into problems because the Flash Player security model does not allow you to upload files without the operation being user-initiated (i.e. a mouse click event is in the stack trace.) There are way to work around this though, e.g. sending the file as an AMF ByteArray through an AMF service, but it might not be future proof.
In the end though, for any type of professional-grade application, you'll definitely want to incorporate a Flash Media Server (or Red5.) There are companies from which you can hire such services, one example being Influxis. Going down that route, you won't have to host the server (which is Java) yourself.
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