It wasn't really a threat, it was joke.  He was kidding around with her, though she thought he wasn't at first.  He wouldn't really discipline her since that is his parent's job, mostly. And of course Sev wouldn't allow it. But he is 9 years older than her, like my brother was with me and my brother often joked around with me, saying if I misbehaved when he babysat me, he was going to spank me, but like Harry, it never went any further. 

Actually, the main theme of this story is doing something forbidden and getting in trouble for it, which was why Harry used it as cautionary tale for his little sister, who has the same impulsive tendencies he does.  If you'll note, both Sev and Harry stress the fact that it's not usual for Severus to discipline with spanking, which is why Harry still remembers the incident and the punishment all those years later. 

As for the discussion of punishments and so forth, my sisters & brother all of whom are much older than me, were quite candid about talking about all the dumb stuff and naughty things they did as kids when they were such and such an age and how they were punished for it, to me and to their own children, so I don't find it strange that Harry would discuss such things with Eileen. 

This story is part of a larger series, Never Again, and if you read the rest of the stories in it, you'll get a much better picture of Harry as a little kid and it focuses a lot on everyday issues, this was simply a piece I wrote to detail one particular incident that was mentioned in the larger novels.