The Fingerprint will be use to open the main door of the B.A.D. Control Center. Inside the Control Center, you’ll find a door with a fingerprint scanner. Since you have the wine glass with the fingerprint on it, you’ll use that to sneak inside.
How to Get the Fingerprint
Once you get the Chef Hat, go back to the table and talk to the B.A.D. operatives. One of them will ask you fill up his glass. He’ll give you a wine glass that has his fingerprint on it.