There are certainly gunners credited with five or more kills. Albert E. Conder's The Men Behind The Guns: The History of Enlisted Aerial Gunnery 1917 - 1991 has a section, "Some of the Aces"; Conder says "The thousands of enemy fighters downed by Gunners were counted as a "team" effort, rather than crediting individual gunners. The AAF claimed that record keeping was to [sic] difficult." He nevertheless goes on to list a number of "aces", including S/Sgt Donald Crossley with 11 kills, S/Sgt Michael Arooth with nine, S/Sgt Benjamin Warmer with nine (seven in one mission) and several others including S/Sgt John Quinlan, tail gunner of the Memphis Belle who later flew on B-29s, credited with five German and three Japanese fighters.

Air-to-air victories are enormously difficult to verify, though, even at the best of times with a small number of combatants and gun camera footage; with large formations of bombers, each with multiple gunners, the number of aircraft claimed downed by gunners was invariably higher than the number of actual losses suffered. Conder gives the total claims of Eighth Air Force Bombers as 6,259 destroyed, 1,836 probables, 3,210 damaged; those figures are likely out by a factor of eight or nine (see [a previous question] (https://www.reddit.com/r/AskHistorians/comments/7sjan2/b17_gunners/) for further details). I'm not sure where Conder gets his individual figures from, but they're difficult to corroborate; [The Unknown Aces of the Eighth] (http://www.mightyeighth.org/blog-post-4/), for example, credits Arooth with "at least 17 enemy planes".

In the RAF [Wallace McIntosh] (http://news.bbc.co.uk/1/hi/scotland/north_east/6726347.stm) had the most claims as a bomber gunner (eight and one probable, though again it's hard to verify), [Peter Engbrecht] (http://www.bombercommandmuseum.ca/engbrechtgillanders.html) of the RCAF claimed five and a half. The highest claiming RAF gunners were those in Defiant turret fighters, particularly those of 264 Squadron; Ted Thorn (pilot) and Fred Barker (gunner) had the highest total, 12. Once again, though, the "confirmed" kills of 264 Squadron are likely too high, not tallying with German losses (for more details on the Defiant, see [another previous question] (https://www.reddit.com/r/AskHistorians/comments/7t2j3j/how_effective_were_aft_cockpit_gun_turrets_in_ww2/)).

I haven't got any details of World War I gunners; Above the War Fronts: The British Two-Seater Bomber Pilot and Observer Aces, the British Two-Seater Fighter Observer Aces, and the Belgian, Italian, Austro-Hungarian and Russian Fighter Aces 1914-1918 by Norman Franks may be of some help.