On Linux it is supported, but has some short comings, but that said, they DO have a SDK for the Decklink hardware and FFMPEG does has support for it but isn't compiled normally for it. I didn't read the SDK license closely, as it might discourage distributing binaries in some form.

But that said, two links below provide enough information on creating a version of FFMPEG with Decklink support and is a DEBIAN styled package