Multiple Partition Keys?
You really don't need partitioning for this to work efficiently, which is what I told you on your last question as well...even if you have billions of rows.

If you cluster on the BarcodeID (which I am assuming is unique) and put a nonclustered index on LoyaltyCardID it should work just fine.  These are NOT complicatd queries with a lot of additional logic from the sounds of things, and simple seek operations are extremely efficient on their own.

Are you getting pressure to partition or is it just something that you have decided to do?