That video isn't very realistic for a chin that isn't used to being hand fed. There is no way you can see what you're doing with a chin in your lap facing away from you.This is a hand feeding video made by one of the ladies on another forum I am on.
I'm right handed so I tip the chin back at a 30 degree angle with my left hand and syringe with my right hand. I usually sit with my left foot propped up on something so I have the chins back resting on my leg and their head cradled in my hand. Also stabilizing their body with my left arm. Some chins you need to put the syringe in the side of their mouth, behind their teeth. Others prefer to have it on their lips. Part of the trial and error of syringe feeding is finding the most comfortable position for both you and the chin. Once you get that figured out, feeding becomes much easier.
As long as they're not recovering from surgery, I give dust baths after feeding. It helps get the CC out of their fur and makes them feel a lot better.