Old post, but I ran to this same issue with some 2960S switches with that FlexStack unit in the backslot.
No, there really was no way to show the serialnumber of that unit. I did go through all show commands related to this unit. Allso "show tech".
Unless it (unit serialnumber) is printed on the unit it self. But see, some units are labeled some units are not. I had 13 stack units, and 5 of them had those labels on them.
It is impossible to see that label without removing that unit.
Unless, you have been bright when receiving that shipment of switches. And you have looked at the boxes of those "C2960S-STAKC= " unit stickers carefully and wrote down the serial that is printed on that cardboard box.
From that cardboard piece, you could salvage the serialnumber to an asset register and save this data there.