Again, to point out, this is quick and dirty maths based solely on the potency of actions, which should be a reflection on the total damage.
Paladin:
GCDs, Total Eclipse, Prominence, Magic Circle, Blade Combo.
oGCDs, Circle of Scorn, Expiacion, Imperator, Blade of Honour (sorry, British, have to spell it right >_>)
Buffs, Fight or Flight (25%), Requiescat.
Total potency on initial target, 8187.5, each additional target 3935. Things to note, there is an extra GCD available under FoF, so there is potential for extra damage over the full duration, but that would just push the damage higher.
Warrior:
GCDs, Overpower, Mythril Tempest, 3x Decimate (IR), 2x Chaotic Cyclone, Primal Rend, Primal Ruination.
oGCDs, Orogeny, Primal Wrath.
Buffs, Storm's Tempest (10%), NOTE: all auto crit/DH took the potency and multiplied it by 1.875 (1.5*1.25).
Total potency on initial target, 6283.75, on all additional targets, 4331.25
Do note that, whilst there is an extra GCD used here, it still comes to less potency than all the other jobs and this is before we take into account crit rate on the other jobs, which only boosts them higher.
Dark Knight:
GCDs, Unleash, Stalwart Soul, Quietus, 3x Impalement, Disesteem
oGCDs, Salted Earth, Salt and Darkness, 4x Flood of Darkness, 2x Shadowbringer, Living Shadow
Buffs, Darkside (10%)
Total potency on initial target, 8511, for any additional targets, 6631.
Notes, I assumed 4 Flood of Darkness and 2 Shadowbringer casts, if you want to adjust values accordingly, you +/- 176 per flood and +/- 660/495.
In the calcs, Living Shadow is not granted the 10% buff from Darkside, I also do not know how the potency is affected because it is classed as a pet, so results might be higher than expected. In total, LS does 2450 potency on the initial target and 1312.5 on any additional targets.
There is also the fact not everything lines up evenly on a minute cooldown like the other tanks, so damage will scale quite a bit between pulls and this is one of the best case scenarios.
Gunbreaker:
GCDs, Demon Slaughter, 3x Fated Circle, Double Down, Lion Heart Combo
oGCDs, 3x Fated Circle, Blasting Zone, Bow Shock
Buffs, No mercy (20%)
Total Potency on initial target, 7644, total potency on additional targets 4560.
Things to note, this has assumed a setup of Demon Slaughter ready to be comboed and having 1 cartridge before starting, so this is close to a best case (with the only improvement being an extra Fated Circle, which, with enough enemies could pull ahead of Paladin, even if we used the last GCD on PLD for another Holy Circle. GNB and PLD are pretty close with GNB being better the more targets you have.
So, to recap, on the initial target, damage goes DRK* > PLD > GNB > WAR and on additional targets the damage goes DRK* > GNB > WAR > PLD
However, since we took different amounts of GCDs to get the raw damage, if we take the average, the order changes to DRK* > GNB > PLD > WAR, do note that GNB and PLD are so close it is a <10 potency difference. If we take these averages and go over multiple mobs, the order stays as DRK* > PLD > GNB > WAR.