RTMP was once proprietary, but was discovered by Adobe some time ago. Therefore, you can use an open source server, such as Red5 , now it should have full RTMP support.
For .NET, I found this library only:
http://www.fluorinefx.com/index.html
I have no experience with .NET, so I don’t know if this is really useful for you. For me, it seems like it is suitable for your scenario.
If this does not work, you can think of streaming using Adobe Media Server through the HLS protocol ( HTTP Live Streaming ). On the client side, this should work on .NET, but again, my knowledge of the platform is too limited.
To provide you with another option, you can use the Wowza streaming server as it provides an add-in that essentially converts the RTMP stream to Microsoft Smooth Streaming (or any other format of your choice) that will definitely be compatible with .NET / Silverlight. If he is smart, he should not really re-encode the bit stream (just recompose it), but I have not tried this.