Dealing with dandruff is the same as dealing with anything else that is not OK in the body.
A good diet with plenty of alkaline foods, good exercise and body hygiene (taking head bath in cool water and sleeping in clean conditions etc) go a long way.
If your water is salty, avoid using that for head bath and use minimal amount of drinking water for head bath. If you can, make arrangements to purify salt water at the source (like the water tank).
The real fix is fixing the lifestyle and hygiene practices.
As a short-term, chemical free, intervention, one can squeeze the juice of one lemon and apply it on the scalp and rub it and leave it for 10 minutes and then washing it off. If it is for children, it may be good to dilute the juice.
Have also heard about effectiveness of Triphala powder paste being applied for 20 minutes on the scalp and then washing it off.