“Is the blinking of eyes a reflex action?”

There are many reasons for increased blinking rate in eyes. We need to rule out medical issues first, such as seizures or thyroid issues, or even eye issues. I would rather have you get him evaluated from his pediatrician first and let him make the decision of who next to see. I generally don’t see this in my practice as it relates to stress.
Hope that helps, please go to the pediatrician.

Blinking is a spontanous action with a frequency that can usually increase with bright light, iiritant agents in the air or eye disorders, i.e., conjuntivitis.
Stress my be also a cause. In, addition, a Blink Reflex can be evoked mechanically by taping around in the forehead or with a short (0.2 or 0.3) elecrical stimulus applied to the supraorbital nerve and recording the response in the Orbiculares Oculi muscles. This procedure is performed using Electromyogaph and provides information of the reflex pathway: Trigeminal nerve (V1) , Brainstem and Facial nerve.

It could just be a tic. If it persists, please have your son see a pediatric neurologist.

Blinking can be related to stress. Also, it can be a tic. Children commonly have a Transient Tic Disorder. However, I can’t answer precisely what it is and he needs to be evaluated by a psychiatrist or neurologist.
Stay safe.