Because the Flash plugin itself controls where shared objects are stored and you cannot (as far as I am aware) change that location nor determine what that location is, there is nothing you can do about this one, unfortunately. You will have to deal with the lost data. It will happen eventually anyway, because I believe shared objects are cleared when you clear temporary browser data (or at least they should be, anyway).
On the bright side, the average user does not know you can switch between plugins nor do they know how. The vast majority of Chrome users, even those with a more technical background, will be using the terrible Pepper Flash plugin, so your scenario should be a rarity.
There is a way around it, however. You could set up a remote server and store the shared object there. That way it is not stored locally and you decide where it is actually stored. I personally can't think of a situation where this would be preferable to having a couple users lose their data, but it might fix things for you.