I honestly can't wait to ask my local retailer what data they have on me based on their loyalty cards. So far they were exempt from data disclosure laws because they were not an IT company.
What if they give you only part of what they know? How would you be able to tell if they know more? And even if you could, how would you convince authorities that something is wrong?
I think we're probably talking about national chains here.
I would imagine stores will use the loyalty cards to profile users, and if they've every stored any of the profiling data then this data will be the data you will be getting.