Thanks to Thump! for posting this information on the ADVrider DR350 Thread. In Thump!'s own words:
My current project is the recovery of a basket case DR350S. It will be an untitled dirt bike with a kicker motor. However I'm planning to use the original steel tank and the OE locking gas cap was permanently attached (no key, buggered lock) so I had to drill it out.
Anyhow, I needed a new gas cap so I went over to O'Reilly's and found this one. It is their Master Pro Select brand model 6023 and it fits pretty well. It also has an internal one way vent so hopefully it will work satisfactorily. About USD $7.00.
Replacement gas cap for the Suzuki DR350; Master Pro Select part number 6023.