Getting a pinch harmonic is a bit of a knack - trying to get it for the first time may be quite hard but once you have the knack it's really quite easy.
It's all about how you hit the string.
The string is actually hit twice ( within micro-seconds ) - once with the pick and then with the part of your thumb that's following through.
In the video I'm doing it with a pick but the technique works equally well with just fingers ( with the nail of the index finger doing the job of the pick and your thumb getting the harmonic exactly as if you were holding a plectrum - or as if you were pinching - hence the name )
You could, if you prefer, start trying this right hand technique with an open string - in which case you should pluck right over the 12th fret.
It may take quite a few goes for the harmonic to come out.
You just have to perservere ( possibly with fine adjustments to the position of the pick and thumb - also make sure you're picking right over the correct fret ) until that magic harmonic comes out at you.
In Tab a pinch harmonic looks like this