There isn’t a legitimate reason for Kizaru to fight Saturn. It’d be nice, I guess, because it fits into tropes we like to consume. But Oda hasn’t hinted at an immediate betrayal. Maybe in the future it’ll lead to that, at least I hope so.
Nah, I don’t want Kizaru vs Luffy at this point. The arcs over, the moments gone. There wouldn’t be much excitement.
I would 100% take a better written Kizaru V. Luffy before the flashback over a well written betrayal from Kizaru, leading to Kizaru v. Saturn though.