No long, I'd imagine. But again there is little to no way to figure out for sure whether the Chinese government has this information. The story really highlights the careless handling of data, because the chances of the Chinese government (or any other third part) getting access to these data is way too high.
What kind of interest would you say the Chinese government has in the health records of a few million Danish residents? I don't know, maybe it's really important, but then maybe it's not that critical after all.