I think Oda will keep Kid around as Luffys Rival for some time. Luffy will take down Kaido (which is considered a bit stronger) and Kid will take down Mom. Both will take the Positions of the Yonko, maybe even take over some of their crew, at least as alliances.
So i hardly assume Kid to beat Big mum. If he kills her, just puts her down, give her to the marines, or beats her into Olin, doesnt matter for me in that case. But Big Mum will be taken out and freed from her Yonko-Position. Like Kaido will too.
I still think its funny how he is literaly called "Kid", while she is Big "Mom". Stupid and easy connection. Also its time to reveal when he was in WCI, what exactly he stole, which he hurt etc..