How do I get this thick and crispy sound on my amp?

Personally, I thought the tone sucked. It sounds like it's coming straight out of a Marshall MG. It sounded flat and muddy, not crisp. The only thing saving his tone was the fact that he had a nice guitar, most likely with Gibson Burstbucker pickups, which brought a little more clarity into it. The thickness you're hearing is probably just b turned up around 6 or 7, as there was only a moderate amount of gain.