Give me an example of anything they can do to big mom.
The Kid pirates are featless so you're asking a redundant question. I've already stated that my reasoning for this matchup is based on Kid's portrayal to Luffy. For me there's not much of difference between saying Kid will face of against Lilin and saying Zoro & Sanji will be facing off against King and Queen respectively. Regardless of how strong people think King and Queen are, Zoro & Sanji will most likely be squaring off against them as they are Luffy's strongest fighters. In the same sense, Kid is one of Luffy's closest rivals and both are in very competitive relationship, so if Luffy beats Kaidou, chances are that Kid beats Lilin.
Like first there's Big mom's iron balloon body and physical strength that bounces off Gear forth luffy. Then there's prometheus
With regards to the Lilin v Boundman clash on WCI, I'm one of those that believes that Boundman wasn't completely ineffective against Lilin as it was strong enough to make her hand rattle. (I don't really wanna go into that argument ^^", so it's fine if you disagree) As such, blunt force might be effective against Lilin. Hell, Queen was able to give Lilin an headache with his attack so I think it's likely that blunt force will be able to get through to her even without stuff like advanced armament.
Also in the current chapter, Luffy said he could end the HBPs ship in one attack, to which Kid also said he could do same. It's important to note here that Luffy used Boundman to take out the fleet. As such, I wouldn't be at all surprised if Kid is capable of using attacks on the same scale as boundman.
It seem you are ignoring the amount of shit required in the plot for the strawhats to escape her. She had to be insane from hunger, Brook had to have a DF that directly counters her df, Nami had to have an ability that let's her steal Big mom's abilities. Multiple people had to betray her. And after all that, the strawhats+sun pirates+ germa+fire tank pirates BARELY SURVIVED.
In a way aren't the Kid pirates even more impressive? :p they were able to perform similar feats to the SHs and did it without all that plot amour and those allies. Jokes aside :p, I doubt they had BM personally come after them but still, the fact remains that the Kid pirates performed similar feats to the SHs on paper.
Now according to you, Big mom without the hunger or people who directly counter her abilities will actually get into a serious fight with Kid's crew? So Kid's crew >>>>>>>>>>>>>>>>>>>> sun pirates+ half of the strawhats+fire tank pirates+germa right?
Because that's literally the only way of saying Kid's crew can do anything to Big mom right? Kid's crew should apparently have Kid at minimum Admiral level and Killer atleast YC2 level and at least 2 YC3 level and 2 veteran level guys.
So what you're saying is that Kid's crew can low diff the strawhats then
Again fights don't always have to be powerlevels ^^" even more so when it is many v 1. The strength of a group doesn't necessarily have to increase linearly it could also increase exponentially depending on the affinity and coordination between them. The Kid pirates could be a group that excel in taking down the big bad together as opposed to the SHs who usually delegate that to Luffy. The fact that they have a circus type theme could potentially even hint to that.