My setup is limited to a Canon 6D and a Yongnuo flash, but I have a feeling this may be more fundamental than just the specific combination of body and flash.
When you set the camera to movie mode, you can still trigger a still picture capture with the shutter release. However, when you do this, an attached flash does not trigger. Why not?
Note, that this setup WILL fire the flash in live view mode.
(If I had to guess: rolling shutter in movie mode makes this impossible?)