To “chat someone up,” in British English, can simply mean to start a conversation, whether or not flirtation is involved. In Nickey’s case, it would seem that flirtation is definitely on the agenda. As for the rhyming slang, the latter matter might scatter the platter… although a flirt would flatter. Still not on Nickey’s list, I suspect.
If you're enjoying Natural Habitat and would like to see it continue, there's a few ways you can help: