Back in the 1920s submarine M2 operated a Parnall Peto 2 seat reconnaissance aircraft. Lts Byas and Keighley-Peach are on record as drawing both flying and submarine pay. Unfortunately, M2 was lost off Weymouth when the hangar flooded.
Photographs at
http://en.wikipedia.org/wiki/Parnall_Peto
No record of whether or how the 2 Lts wore their badges.