The slice of cake is not an item redeemable for KS. As per the instructions in the
Grab Bag section of the Birthday Pets Chart:
"Each year staff members make a pet to celebrate their own birthday or some accomplishment. There are a few different colored sliced of cakes in bags, and each one means something different. They allow you to choose a birthday pet from previous years, based on which color slice you got."
I believe each slice of cake contains the name of a staff member within its URL? (Baal, Kodai, etc.) Depending on the staff name given, you may redeem that slice of cake for a
staff birthday pet corresponding to that staff member from previous years.
In your case, according to the records, your slice of cake is representative of Kodai, which means it could be turned in for one of her pets, such as the
Observe Sabbit.