There is no way to do anything efficiently with compressed air.
Compressing gasses is one of the most irreversible forms of energy storage you could name. When you compress air to, say, 10 atm., it gets almost hot enough in the cylinder to ignite a fuel (diesel engines typically run between 14:1 and 20:1 compression). That hot air then loses heat into the compressor parts and tank, until it's back to ambient temperature.
Then, when you let it expand again (say, though a piston engine like a steam engine, or a vane motor or turbine) it gets very cold, cold enough to form ice if the flow rate is high enough.
Beyond that, you squeeze water out of the air as you compress it, and this water condenses inside the storage tank when the air cools, with the result that a compressor tank fills with water over multiple fill/drain cycles -- but if the tank is kept drained, the discharged air will get even drier as it expands and cools.
As noted in comments, for a Kelvin Thunderstorm Machine, you need a conductive working fluid, but if you have a way to bias the air flow with high voltage ion emitters, it ought to be possible to build something that works more or less the same way (except it probably can't be made to self-start; you have to have a piece of glass rod and a silk cloth to produce a starter charge). Air is conductive, at least for ionic flow at high voltages. If you can once get a charge on your biasing points/rings, you should be able to separate charge with ion flow induced by the movement of discharge air.
Will this be efficient? Absolutely not. The most efficient way to use compressed air to generate static electricity is to use a small air motor to run either a Van de Graff or friction-free Wimshurst machine. And this is none too efficient; steam would do a far better job here, if you have a way to boil water.
The one exception here is if your compressed air is free. Sure, There Ain't No Such Thing As A Free Lunch, but if you have a significantly hydraulic head available, you can use the power of falling water to directly compress air with a device called a "trompe" -- this works by entraining air into water flowing downward, when routing the water though a chamber where the flow slows enough for the air bubbles to separate. The head above the trompe can be close to that of the infall -- so if you have fifty meters of drop, you can get close to five atmospheres of air pressure, and once the trompe is built, it operates without further intervention. Draw too much air, and you'll get water in your air pipes, and that's really the only significant problem with the trompe (the compression and decompression dry the air, despite having been bubbled through water during compression).