The Blackmagic Television Studio (TVS) has a built in H264 encoder for the Program bus output. It provides this via the USB 2.0 port (Note: the new HD and HD Pro do not have this capability). The BMD H.264 Pro Recorder has the same capability and can be used with the software below.
Blackmagic Desktop Video utility can capture this but the file is very big and you have to wait until you stop and save the file before you can access it. If the software crashes then the content is lost. This solution also doesn’t allow streaming the content in real-time.
There is a good 3rd party product, MX Light http://mxlight.co.uk/ that many people use for streaming which you may want to evaluate.
MXPTiny is an open source solution worth considering. I have found this to be very reliable and it creates a file that can be read by other applications such as VLC or ffmpeg at the same time as it is being created.
This version https://github.com/FlsZen/MXPTiny/ was created in Dec 2015 from a fork of the original project created over 4 years. I have found this new version it to be reliable with the latest BMD drivers (ATEM 6.8 and Desktop Video 10.7 – must be installed on same computer as MXPTiny).
Update: Also works with DesktopVideo driver 10.9.5 and H.265 Pro Recorder (previous driver would not detect USB device).
I have made a compiled version available here (updated to release rather than debug build)…
It requires that you also install the required Visual C++ Redistributable for Visual Studio 2015 x86 or x64 (install the x86 version even if running 64bit OS). Only tested on Windows 8.1 and 10.
If MXPTiny reports no device found, try running C:\Program Files (x86)\Blackmagic Design\Blackmagic Desktop Video\BMDStreamingServer.exe