How to lock and scroll image, using smartphone green screen mockup?
You will need to:


track the motion of the screen, using whatever tracking tools you have at your disposal. A 3D track or a corner pin type track will both work, because it's a flat rectangular screen. The quality of the track is what will sell this shot.
key out the green screen, using whatever keyer you have. Looks like a good key, so you shouldn't have too many problems
create the animation of the screen scrolling. This is probably best to do manually using keyframes, perhaps with the original video as a guide layer if your software allows it. There is no point tracking the movement of the fingers, as the scrolling continues after you flick with your fingers on a phone screen, so it has to scroll independently.
composite the app screen animation behind the original layer, using the tracking data to fit it to the original screen's position, size and rotation. You might want to add additional layers to the composite: e.g. a subtle reflection layer would help sell it.