Ok I got this. You cannot notice the movement jittering if your display is running on 60fps, but on 165 for example it is noticeable
Ok, seems like this issue appears only if your display fps is higher than _physics_process frequency. You can try it out by lowering _physics_process frequency in the Project Settings -> Physics -> Common -> Physics FPS. For example you can set this value to a 10 for example and see how movement become jittery.
This page tells:
Godot 3.1 does some improvements to this, from allowing kinematic bodies to be animated in the regular _process loop
So I think that the affirmation like "Kinematic body movement should be handled in _physics_process only" relates to versions below 3.1