I have a database of [OpenFlights][1] data laying around from [What's the quickest route between antipodes using regularly scheduled transit?][2], so let's put it to work.

[an excruciatingly boring period ensues wherein we discover that PostgreSQL got upgraded on my system, leaving a database that is incompatible with the new version, and entirely too much nonsense is involved in sorting it out.]

After preparing a scratch table:

> SELECT ST_X(source_geom) as src_x, ST_X(destination_geom) as dst_x,
> abs(ST_X(source_geom)-ST_X(destination_geom)) as delta, * from flights
> order by delta limit 20;

For some reason, OpenFlights thinks that "Illinois Airways" operates a flight that both arrives and departs PKN airport in Indonesia. We'll remove that, along with duplicate/reverse city pairs, including those operated by multiple airlines/codeshares to get a few top results:

> '-68.2080993652344','-68.2043991088867','0.00370025634765625','Air
> Canada','YBC','YYY'
> '106.652000427','106.65599823','0.00399780299999009','Vietnam
> Airlines','CGK','SGN'
> '-81.7552032470703','-81.7595977783203','0.00439453125','Silver
> Airways (3M)','EYW','RSW'
> '-2.90027999878','-2.90499997138977','0.0047199726097702','Linhas
> A','KOI','PPW'
> '-111.983001708984','-111.977996826172','0.0050048828125','Delta Air
> Lines','SLC','HLN'
> '-94.0650024414062','-94.0708007812','0.005798339793742','Canadian
> North','YEK','YYQ'
> '139.779999','139.785995483','0.00599648299998989','All Nippon
> Airways','HAC','HND'

This gives our winner, flights between [Baie-Comeau Airport][3] and [Mont-Joli Airport][4], both in Quebec, Canada. FlightAware tells me this is Air Canada Jazz [JZA8968][5]/[JZA8964][6], nearly a straight shot north-south across the St. Lawrence River, a [distance of 59km][7] and a difference of just 0.0037 in longitude. 

This is entirely based on the coordinates of the airports in the OpenFlights database, not the actual route of the flights, which will vary due to the usual flight planning considerations.

**Update**: I was curious what happens if instead of directly comparing coordinates, we go by azimuth instead, as JonathanReez sugguested. This method gives us [CGK-SGN][8] (Jakarta-Saigon), the runner-up from the coordinate-based approach, with a bearing between the airports of 179.986. 

This approach also produces candidates with greater degree differences closer to the poles, such as [YQR-DEN][9]. The bearing is -179.970 even though the coordinate difference is about 25", since the lines get closer together as you approach the poles.


  [1]: https://openflights.org/
  [2]: https://travel.stackexchange.com/a/69591/13650
  [3]: https://en.wikipedia.org/wiki/Baie-Comeau_Airport
  [4]: https://en.wikipedia.org/wiki/Mont-Joli_Airport
  [5]: http://flightaware.com/live/flight/id/JZA8968-1513057027-airline-0114
  [6]: http://flightaware.com/live/flight/id/JZA8964-1513057008-airline-0031
  [7]: http://www.gcmap.com/mapui?P=YBC-YYY&DU=km&SU=mph
  [8]: http://www.gcmap.com/mapui?P=sgn-cgk&MS=bm&MP=ortho&DU=mi
  [9]: http://www.gcmap.com/mapui?P=yqr-den&MS=bm&MP=ortho&DU=mi