Possible, but saturation would be the main obstacle
Flywheel/gyroscope based attitude control changes the angular momentum of the air/spaceship by increasing or decreasing the speed of the wheel. That works fine for small changes back and forth, or keeping a certain stable attitude against small forces. But even in spacecraft the gyroscopes eventually reach maximum speed, at which point they can only exert force by slowing down, in the opposite direction of what has been needed most.
This is corrected in spacecraft by slowing down the wheel and compensating the unwanted force with thrusters, using up fuel supply to de-saturate the gyroscopes.
In the atmosphere the main differences are that the forces exerted by wind on a ship are much greater, but drag also slows down any rotation eventually.
For airships there is good news and bad news. The bad is that trying to maintain attitude against constant aerodynamic forces (wind) will saturate the flywheels very quickly. This makes them useless as the primary attitude control system. They could be useful for a "quick" combat turn since the flywheel would be used both to start and stop turning resulting in little net change, but from there other controls would have to keep the ship in position.
The good news is that the wind and aerodynamic surfaces can be used to de-saturate the flywheels without the whole battleship having to spin around like a top or expend fuel.
If the ship saturated the flywheels steering to starboard, they could either be used for a (very predictable) turn to port or the ship could be turned such a way that the wind is turning it to starboard more, then using the flywheels against that to de-saturate them.
Regarding the technological requirements: flywheels are not complicated, but the sheer size and mass of battleship-turning ones demand a high level of engineering skill to make them somewhat safe and reliable. Very strong supports and especially bearings would be needed. A jammed bearing would probably cause the wheel to tear the ship in half, while a damaged support would let the wheel run wild inside the hull. Neither sounds very attractive, unless you are the enemy.
My guess is that WW2-era engineering would be up to the task. A whole battery of smaller flywheels might be achievable with late WW1 engineering, but if they're not close to the ship's center of mass, they would make the ship harder to turn.