What I do for Oliver my Orange Wing is I file his beak and then rub a drop of coconut or olive oil on his beak to keep it looking nice and smooth.
But just because it will look healthy because you have add oil on it don't tell that it is healthy. That is only to hide the problem.
To add oil on a beak can also make it very unhealthy because the beak can't regulate moisture anymore.
If you must add oil on the beak, do it very spare/rarely and always when it's wet.
Flaxseed oil is good, but should be added on the food, not on the beak.
I will say a good varied diet, real sunlight and regular bath will make him and his beak healthy.
That will also make him have better and shorter molting periods.