Law never intended to take down Kaido, though. In Dressrosa he revealed that was a lie to bait Luffy into helping him.
His only plan was to screw Doflamingo so Kaido would kill him (Law didn’t even expect to bring Doflamingo down himself, he was expecting to die just in an attempt to make him in bad terms with Kaido so Kaido would finish the job).
I would say the fact Law sticked around after Dressrosa to help take down Kaido was already a huge show of gratitude, because he was carrying down his (originally false) promise to repay Luffy for taking down Doflamingo.
Any explicit show of gratitude would have come back then in Dressrosa (I don’t remember if it happened), not now.
As for Kid, you can see the change through his actions. There’s a point in the fight against Big Mom when he and Law say they are intending to die there only to prevent her from going help Kaido (so basically admiting Luffy was the strongest there and their place was to do what was in their power so he could succeed). I don’t think a bigger show of acknowledgement of Luffy can be given without betraying his personality.