To do the pinch harmonic, you need to hold the pick in a way that will let the edge of your thumb hang over.

When you strike the string, the edge of your thumb (on your picking hand) must strike the string at the same time the pick does.

You need to find the sweet spot though, they don't occur in all places, so when you strike say the G string 7th fret, strike the string with your pick and thumb and continue to do it up and down the string (around the pickups) until you get a good harmonic.