#1
How exactly do you do these? I know you use the pick and the skin of your thumb to hit the string at the same time but I can seem to make it squeal when I do this.
#2
Practice. Also you get different tones from the harmonic depending on where you strike the string in relation to your pickups. So you can strike closer or farther away from the neck and find the sweet spot. Also, use some vibrato on the string you're fretting. Then it just comes down to your pickups, amp gain, etc.
#3
Crank your gain in the beginning and just practice some technique videos. I struggled with pinchies at first, but imitating Zakk Wylde did me a favor!
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#4
Quote by squilly_willy
How exactly do you do these? I know you use the pick and the skin of your thumb to hit the string at the same time but I can seem to make it squeal when I do this.

This is better off in Guitar Techniques but anyhow. Hold the pick as normal, bend the pre-knuckle in your thumb, this will naturally angle the pick downwards. Now pick the string confidently.

As mentioned earlier, experiment at various points along the string and over the pups.
#5
Wikipedia to the rescue! When you play an harmonic, you divide the string into equal parts. The first harmonic, the open 12th fret harmonic, divides it in half and you get an octave jump. If you want an octave pinch harmonic, you pinch right in the middle between the fret and the bridge, so a 12th fret octave harmonic means you pinch over the 24th. And you can pick up the rest from that article...

As for the technique, it's really just a matter of practice makes perfect. I suggest pinching the open string 12th fret harmonic. If you can perfect your technique on that, all you need to work on is judging the correct spot on your string based on which harmonic you want to hit!
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#6
You kinda flip your hand to get the effect. Stillborn by BLS can get you help in the tones, because Zakk doesn't do the Pinchs on the same place. Also practice on every string, I can do em on most of my first.