This might be a really basic question, but how would my right hand pick this part really fast?
With the first 3 notes I pick them down, up down and move to bottom string but then down, up, down, up, down up? That kind of ruins the flow since it ends on an up and I have to move to bottom string..Is it just a question of practicing it until you get it or is there a better way?

Fuk been playing for like 11 years and never payed attention to actual picking techniques lol

I seem to find it helps if I say 'tri-per-let' as I practice them. Maybe it's just me?
A combination of alternate and economy picking will get you there.
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You CAN play anything with anything....but some guitars sound right for some things, and not for others. Single coils sound retarded for metal, though those who are apeshit about harpsichord probably beg to differ.