I think we have a winner. I only managed to come up with
CHC - LERO: 12404 mi
Christchurch [Intl], NZ - Lugo (Castro de Rey) [Las Rozas], ES
On the other hand: ARI-SYX are not exactly on opposite ends of the globe (about 2 minutes NS and 15 minutes EW), so some longer distance might be possible on great circle mapper...
HTB.
Edited to add: For example:
0°0'0"S 0°0'0"E-0°0'0"N 180°0'01"E with 12451 mi. Does this qualify as a valid flight -- two aircraft carriers would come in handy...
Not seeing anything though with the airport database I used to calculate the others. Here's a list of all airports >12400 apart (my calculation is slightly off of GC's). I need to figure out how to calculate spheroid distance vs sphere distance.
Code:
AFA-YCU 12401
AKL-SVQ 12402
BDA-PER 12402
CHC-LCG 12402
CNQ-WNZ 12403
IQQ-ZHA 12403
SMR-XCH 12403
AGP-AKL 12404
CZX-SFN 12404
BAQ-XCH 12405
MAD-PMR 12405
AOR-CIX 12406
CIX-LGK 12406
KTD-CWB 12407
LGS-YCU 12407
UAQ-XFN 12408
BHI-TSN 12411
HKK-VGO 12411
MZV-TFF 12411
AGJ-XAP 12412
OPO-WSZ 12412
MDQ-WEH 12414
VGO-WSZ 12414
MMD-CWB 12415
GRX-TRG 12416
KKE-TNG 12416
HKK-SCQ 12417
VLL-WLG 12418
GIB-WRE 12419
SLM-WLG 12419
MMD-JOI 12423
SYX-TCQ 12423
AQP-DAD 12424
PIO-REP 12426
ABC-GIS 12428
KTD-JOI 12429
NKG-SFN 12430
CIX-HDY 12431
ARI-SYX 12433
TNG-WRE 12434