so what i can gather from Kilgore is that he heats up his mini guns but doing a move or special that uses them and then holding down the HP button prolongs it. So like say you do Kilgore's grab, he smacks you into the air and automatically does 2 shots as you're in the air, holding down the button makes him fire off more shots while also heating up your guns. Once at full heat your guns will do Cinder like burn damage as well as increase the combo potential at the cost of safe range, your phase dodge teleport move, and what i think to be you take more damage... i think.
Kilgore can cool off his guns by either not using them for a full 8 seconds, manually cooling down by spending a bar of shadow [this counts as a shadow cancel so you can do backwards frw. Hp Shot Spread into Cool off into his gattling rush for a confirm combo] or doing his Cool Off Ender which acts sorta like TJ combo's reset ender only not as quick.
Kilgore has also got missiles which he can either just shoot off normally or make a track to position kind where he selects a spot on the stage and the missiles will go that location, even spinning around off camera to come up behind. It's a great defense tool for they can still hit the opponent even if Kilgore is getting comboed.
Ontop of all of this Kilgore seems to have three command normals, one where he shoots both of his miniguns forwards, one where he does a sweeping upwards arch with his shots, and one where he shoots at the ground. The Ground shot move is interesting for it OTGs the opponent. the only other character who can do that is RAM [and Tusk if you really want to count his skewer as an otg even though he can't follow it up unless he gets a counter breaker]. Still unsure if Kilgore can combo after that down shot into a Shadow Gattling Upper, but hey we know that he can tack on some extra damage at the end of a combo.