Yamato doesn't believe Luffy can beat Kaido:
What's going to make her change her mind?
Like she knows Luffy went to fight Kaido and she doesn't think he can win by himself.
Yamato growing up with Jack is still headcanon.
The fight is not happening.
Jimbe and Linlin do not have Yamato and Kaido's relationship. Jimbe has never said he wanted to fight Linlin.
And what will be the impetus for her to do so? What is going to make Yamato put her faith in Luffy?
She doesn't believe that Luffy can win against her father, and Luffy proved her right. She isn't going to stop fighting Kaido randomly. She isn't fighting Kaido for Luffy.