Kidd will sail off from Wano with the same status of Luffy, this is the only thing I'm sure about.
Will he do so by taking down Linlin? Probably, at this point.
Kidd's backstory is more related to Kaido seen what happened to him and his crew cause of him, but Oda made sure to place here and there other connections with Big Mom and also a mistery (the stolen item).
Also, after this chapter, Luffy defeating Kaido is basically confirmed, so Kidd taking down Linlin is the safest bet (not kill tho).
Anyway, the war has still a long way to go... Calamities are not even set and the majority of the Tobiroppo fights haven't even been developed yet, so a lot of changes can still happen.
To answer those who think that Linlin can't fall here cause there's not the full crew: Oda made sure to bring Perospero, Smoothie, Snack, Daifuku etc... aka the Big Mom Pirates who had less focus in WCI and were not properly defeated (unlike Katakuri, Cracker, Oven (in a way), Bobin, Opera etc... who stayed in WCI).
To me, seems like Oda wants to defeat the remnants here in Onigashima so that the Big Mom Pirates are 'officially defeat', the same way all the Beast Pirates will be defeated.