Nitrous works well in a piston gas engine because the mixture is in a rather narrow range.

The turbine engine runs much leaner, and with a varying mixture.

Propane would work better, but seriously, a jet engine is expensive, and the parts are in many respects more fragile than in a piston engine. Why risk damage. But if it were the end of the world, and I had to get out of Dodge, I would rig up a propane injection at the inlet, and not tell the FADEC.

Nitrous works well in a piston gas engine because the mixture is in a rather narrow range, and additional oxygen can be utilized with a mixture that gets enrichened, plus has added oxygen. In effect it creates the equivalent of an inlet boost, because it adds available oxygen.

The turbine engine runs much leaner, and has a wide mixture range which supports combustion. Since turbines normally have extra oxygen, they would not benefit from the addition of available oxygen. At least not the way that a piston engine with a enrichened fuel mixture would.

So the net effect of injecting nitrous into a jet engine would be very small, and at max power settings, it would still be small due to the inherent lean operation and associated oversupply of oxygen in the combustion chamber. In other words, adding oxygen when there is already plenty there provides little benefit.