Hi Johannes,
I was about to write that I thought cowboy's static handler should handle streaming by default, but I also decided to google around, and it appears that the problem is that it expects support for the range header, which it doesn't look like cowboy's static handler does by default. It streams it with sendfile, but it doesn't actually chunk it and deal with range requests (as far as I can tell from glancing over the code).
Alternatively, you could try using Yaws as a backend and see if it might support streaming by default - I have no horse in this race.
I haven't personally dealt with streaming video, so I don't have a ton of insight, but I'm here to help in any way.
Hopefully this at least helps to point you in the right direction.
-Jesse