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I have heard that the Dimebag Squeal can be done only on Floyd Rose, though I haven't tried on a regular one though.
Yes you need a tremolo of some sort; play a note, depress the tremolo (this will slacken the strings); catch the nearest natural harmonic, pull back on the tremolo, distortion and reverb will help you get the Dime sound.
Check out this video from the man himself
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