I'm a visual effects artist, as well as a pilot. For analyzing this video, I'll put my VFX hat on. I've made a huge number of films, you can look it up.
1) Given the orientation of the plane in the video, it has to be at least seven or eight miles away (altitude of 30,000 ft or so, and at a significant horizontal distance as well). If you look through seven miles of atmosphere, you cannot see anything black -- blacks become blue due to Rayleigh scattering.
https://en.wikipedia.org/wiki/Rayleigh_scattering
Note that the sky is actually black, but the scattered light from the sun makes the sky appear blue.
Now, ok, say that they processed the footage to bring down the bluish-blacks to look more black? I don't know why they would do that, as it makes it look less real, but if they did it would be very noisy and low-contrast.
2) Tracking the relative speed of the smoke plume to the plane isn't that hard. The span of the plane in one of the frames is 74 pixels. As the span of a A321 is 117 ft, that means each pixel is about 1.6 ft. During a half-second the smoke drifts back 37 pixels, or 116 ft/sec (80mph) if the plane was directly above the camera, or 232 ft/sec (160 mph) if the plane was only 30 degrees above the horizon. We know that the plane was going far faster than that.
3) It appears that the footage was filmed on a smartphone that was pointing at another LCD screen, perhaps even two generations of re-filming. Several instances show quick pans where the plane doubles-up, as if the camera was out-of-sync with the screen it was filming. The very strong contrast between the middle of the screen (pretty bright) and the edges (quite dark) leads me to believe that the smartphone camera was quite close to a cheap LCD screen, which has big variations in brightness with viewing angle.
The blackness of the smoke at a distance of many miles, and the slow speed of the smoke relative to the airplane lead me to believe that this is shoddy visual effects work. It could easily have been done by anybody during the 24 hours between the crash and the release of the video.