This is an example of a Flight Surgeon's badge from from the Imperial Russian Air Service.
These particular badge belonged to Lt. Col. K.N. Finne. He served as the Senior Flight Surgeon for the Imperial Russian Airship Squadron and assisted with Igor Sikorsky during the development of the Il’ya Muromets. He detailed the accounts of Sikorsky in Russia during this period in his book, "Igor Sikorsky: the Russian Years."
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.