For the do-it-yourselfer at home, the basic sound is a combination of humbucker pickups (Gibson Les Paul, PRS, etc.) and heavy pre-amp overdrive (crank the preamp up and turn down the master volume). Something like an MXR Dyna Comp pedal out front set for mucho sustain probably wouldn't hurt either. Oye Como VA!
BTW - I still remember seeing Carlos get wiggy with an old EchoPlex EP-3 at a New Year's Eve concert at San Francisco's Cow Palace back in 1976-77. I can truly say that nobody ever worked that thing quite like he did in creating a feedback loop that went up, up and away for a mind-blowing experience. Syke-a-delic, fer sure.
Now, what I'm describing above is how you might go about getting *that* sound at home, on the cheap. The way Carlos gets *that* sound, inasmuch as I read this in a GP interview with him, depends on a specific soundcheck technique, where he will crank up the volume on his amps, then walk around the stage/recording space until he finds the "sweet spot" where his guitar is right on the verge of feeding back. He then marks a cross on the floor with gaffer's tape, and when he gets down to performing/recording, he basically moves in a tight area around and on top of that "sweet spot" so he can milk the sustain as he needs to.
Unfortunately, this is usually hard to do at home without getting the cops called on you. I still think, for my money, a PRS or Les Paul played through a vintage Marshall JTM-45 amp with master volume modification would nail it. I've never been a Boogie fan, I'm afraid, as they're somewhat of a one-trick pony. YMMV