Well, we do not know whether KIr knew Akai's phone number. All we saw was Gin forcing her to call Akai. It was then interrupted by the hotel case and when it comes back to them, Kir's already online. A possible explanation(of course, I do not have any prove)is that Gin gave her his old contact number as Rye.
Let's hope that Gosho does an epilogue/flashbacks and explain all these flaws.