Is ColdFusion the right choice?

ColdFusion could be a part of this solution, but I doubt it is the only one.  But you have some more basic tasks to understand first.

What do you mean by "real time".

What do you mean by "stream".

Both of those are not concepts normally thought of with web sites.  The HTTP protocol is stateless.  A browser makes a request of a web server, the web server sends a response and then promptly forgets anything about that request and the browser that made it.  In other words, the web server has no way to send any more information to the client until such a time as the client makes a new request.  This makes pushing data to stream it real time or otherwise pretty much impossible.

One way around this is to use client side scripting, like javascript, to have the browser make repeated requests to the server for updates, like every second.  Using some AJAX concepts you can do this in such a way that the browser is not requesting an entire page every time, which saves trendmensly on bandwidth used.

You can think outside the browser, which sticking with Adobe products would most likely be Flex and|or Air technologies to create a Flash based user interface that can make and maintain an open connection with the web server through AMF so that the web server can push new data to the client.

With either of these options, it is quite possible that ColdFusion could provide a middleware layer getting the data from what ever source is providing the data and pushing it out to the client.  It is very good at sitting in the middle.

But until such a time as you have a clearer understanding of your actual application and its requirements and how that works with the internet protocols you are going to have a very difficult time determining what technologies or products would work best.  And trying to do the latter before doing the former could be a very expansive way to go about this.