If you are feeding your child milk, cereal, or any processed food you are likely already feeding them supplements and chemicals.
ALso, technically, all food is of a chemical nature. Life is a series of chemical reactions. So saying something as "chemicals" and therefore "bad" is not all that helpful.
What is important is to understand which foods and supplements lead to a healthy diet and provide those.
For example, it is nearly impossible to get enough Omega-3 without having a very high fatty-fish diet. The key with this is you want to have a balance of Omega-3 with Omega-6, and most of our diets are very high in Omega-6. So taking Omega-3 makes sense.
Vitamin-D is also a big one - especially if you live far from the equator. Unless you are willing to sit outside with your shirt off 1/2 hour a day, you are not getting enough. If you drink milk it is widely supplemented, otherwise, you should take some.
So, those are some arguments for individual supplements (the ones I think are most important). There are many more arguments for other individual ones, and you'd have to learn about them individually to understand whether they might be good for your child or not. There is no blanket answer to "are supplements good to take?".