Really! I call Bum Gouge on that one. (I am so excited, Brett caught dispensing Bum Gouge

) I have seen it many times. SWO- NFO/Pilot, NFO-Pilot, Dolphins-Flight Surgeon. In fact, the current CO of the NRD I support wears both SWO pin (earned while ships company on a disassociated tour) and his NFO wings. I knew two guys that were former Army Aviators that wore their Army wings and Naval Aviator wings. You wear the current one in its proper place and the former one on the pocket flap, if I recall.
I'll see your bum gouge and raise you one.
Per the regs:
Authorized Insignia. The listing below constitutes those breast insignia, alphabetically by category, authorized for wear on the naval uniform. Breast or qualification insignia of other services shall not be worn.
<Insert entire list of every Navy warfare pin insignia imaginable here. NA and NFO are in the same category - Aviation Warfare>
(3) Personnel with multiple qualifications, may wear two insignia, placing one in the primary position and the second in the secondary position, within the following guidelines:
(a) Only one insignia from any single category of insignia listed above <(paragraph 5201.2.a.)> is authorized for wear at the same time.
(b) Warfare qualification insignia take precedence over other qualification insignia and are placed in the primary position.
(c) Two warfare insignia, each from separate warfare categories, are authorized following these rules:
1 The warfare insignia of the specialty in which currently serving will be worn in the primary position.
2 If not currently serving in a warfare specialty, or have not earned the warfare insignia of the specialty in which currently serving: officers will wear the insignia corresponding to their designator, otherwise the warfare insignia earned first in the primary position; all other personnel will wear the warfare insignia earned first in the primary position.
This is why guys like me get two - Aircrew (Naval Aircrew and Marine Combat Aircrew) is it's own category, and also why you see guys w/ wings and SWO pins (and Merchant Marine Sea Chickens).
Later:
(a) Enlisted personnel who qualify for insignia, and are subsequently advanced to officer status continue wearing the enlisted insignia until qualified for a corresponding officer insignia; then replace the enlisted insignia with the officer insignia.
Since there is no corresponding officer insignia for Aircrew, all former aircrewmen continue to wear them as well.