Kid's fruit is like Cracker's fruit in that it uses very little stamina to stall because he can create and rebuild constructs, Luffy has to dodge or tank the blows with his body, Law can teleport while Kid has agro on him. Comparing rates of stamina exertion from Luffy fighting Kaido 1vs1 to these two taking pot shots against her in a controlled situation with great fruits for co-op play is a bit unfair to begin with.
Kid and Law were not fighting against Big Mom for the the 20-30 minutes (several 10s of minutes according to the Japanese Raw) that Luffy vs Kaido post 1010 occurred during. During this time Luffy's stamina consumption was so great that he was knocked out for a second time due to fatigue from a 30 minute 1vs1 of "sloppy" CoC usage (Zoro's sloppy usage burnt through his life force in a few minutes), he was so fatigued upon waking he couldn't physically move, like he was against Lucci or worse, he ate enough to move and fight, not to restore him to 100% or anywhere near that, Yamato in the Japanese raw makes this clear that Luffy is barely standing, coming back here in this state to heroically defeat Kaido.
Kid and Law were not fighting against Big Mom for the the 20-30 minutes (several 10s of minutes according to the Japanese Raw) that Luffy vs Kaido post 1010 occurred during. During this time Luffy's stamina consumption was so great that he was knocked out for a second time due to fatigue from a 30 minute 1vs1 of "sloppy" CoC usage (Zoro's sloppy usage burnt through his life force in a few minutes), he was so fatigued upon waking he couldn't physically move, like he was against Lucci or worse, he ate enough to move and fight, not to restore him to 100% or anywhere near that, Yamato in the Japanese raw makes this clear that Luffy is barely standing, coming back here in this state to heroically defeat Kaido.
Considering how much time Luffy was out of the games, Kidd fought for more time than him no doubt.