That's something else. That's a distortion in the song because of the way the software EQu is handled. IDK the specifics of it, but it's not driver flex.
There could be an explanation for driver flex. When you insert the headphones into your ears, it creates a seal with your ears right? Better seal = better sound. But a seal also adds pressure from your ears (and the drivers). When this pressure is added, the drivers move back (away from your head) until there is a way for it to displace the air (silicone is breathable, so that normally does it eventually). The other thing that does it is the vent in the back. When the air is displaced, the pressure is relieved, you still have the seal, but the pressure is equalized. If this explanation is incorrect, let me know why. This is all theory (but it does answer everything you hear). The clicking is the driver moving (and coils, and wires, and sometimes the actual silicone if you just released the headphones cause they compress due to the force of your finger, then decompress).
^^Again, I'm not professional on this, but that is what I see happening^^