The file in the video is a Nicholson, but it could be any file that's wide enough to accept two blades at a time when sharpening a 3 blade head. (method works for all 3 blades)
Mill Bastard Cut is the most commonly found file that big at hardware stores. I prefer "Smooth Cut". It makes a much finer finish than the bastard, but of course doesn't remove stock as quickly.
I like Grobet files for there quality of cut, sharpness, and longevity. Someone once told me you could file the teeth off a Nicholson with a Grobet. Of course I had to try it.
My experiment didn't do either file any favors, but the Grobet won for sure.
Since the video was made I've replaced the stone with one of comparable size by Norton. Both stones had two grits.
With stones I've found bigger is better for me.