I'm not aware of people doing much beyond a visual inspection and functional test to make sure that the contacts still work. The functional test is either using a test button, or by pumping air into the Buchholz to lower the oil level. The pump used is nothing special.
Seems that if you are a NERC registered entity subject to PRC-005, you'd better figure out a method of testing. A visual inspection, or pushing a button to close the contact would be considered adequate to check the device. Pushing the button would verify the tripping path, but not verify the flow sensing mechanism per Table 5 of the standard.
There is a European Standard for Buchholz Relays-EN50216-2 (2002).As per clause 7.2 "Relay shall be provided with a device to check the operation of alarm/trip contacts independently" In service conditions, only checks usually done are-successful operation of this testing device and alarm contact closing when oil is emptied partially. Condition of terminal connections and terminal box are also important. Additional tests (pressure, vacuum and trip at flow rate of 1-2metre/s ) can be done at any lab or at the works of relay manufacturer. Of course these are superfluous.
I will tell you the procedure what we use to do in India substation projects.
You can hold a can or bucket below the bucholz relay so as not to waste the oil. CLose the valves in both sides of relay so that during testing oil shall not come into relay from tank or conservator.
Open the drain plug located in bottom of relay and soon oil will start flowing out.
When oil comes below alarm contact, alarm gets activated and when oil is fully drained, you will get trip activated.
After testing, close the drain plug and open the valves so that oil gets filled inside the relay again.