Break in on most modern bikes is the first 1000km, and first service is an oil and filter change, plus a general check of the motorcycle. If the bike is at 3000km then it is definitely past the break in.
That said, I've never bought a used vehicle, but if I did the very first thing I'd do is change the oil & filter. Maybe it is I don't trust people, but I'd want to make sure it was done right by me and have an actual starting point on when exactly the last change was. Cheap insurance, so to speak.
After that, you can either go by the mileage intervals in the manual, or at least make sure you change it once per season (if you don't hit the interval), preferably before putting the bike to sleep for winter. I don't know the ZX6R specifically, but I know on my CBR650FA, Honda only calls for a change once every 12,000km using regular oil. That number does seem a bit high to me, but then I never really put more than 5000-8000km on the bike in a season, so that's what my interval works out to be.