Zinc oxide is the ingredient most used for diaper rash creams and it can also be used for coloring cosmetics. I have not seen it on the list of ingredients for any dandruff shampoo that I have used. It has gotten a bad rap lately because people claim that the nano particle size zinc oxide will be absorbed into the skin. I have read a couple of published research papers that disagree with that statement. The people who claim that it can be absorbed in the skin at the nano side have never used peer reviewed case studies and I can't find any supporting their claims.
Having said that, I am not a scientist and have never experienced any problems using it but I use it in rash creams that I make and have never used it in or heard of anyone using it in shampoo for dandruff. You might want to go to the "chemist corner" website and do a search for your information there. It is a website devoted to all things for cosmetics. It can be a little overwhelming because they use a lot of scientific terms but you should still be able to understand everything. If it's not there then it has never been tried by a cosmetic chemist.