It depends on which vaccine you are talking about. Several different ones exist.
.......................... But the general pattern is that you have to give it before the chicks have the problem. If they already have symptoms of Mareks or Coccidiosis or Fowl Pox or whatever, it is too late to give that vaccine to those chicks. But if the adult flock has a disease, it can sometimes be a good idea to vaccinate new chicks against that disease to help protect them.
Good post!

Some others are good also.
what are the reasons I should vaccinate?
If you have a history of a specific disease in your flock you might want to investigate vaccinating for that specific disease. If a specific disease is prevalent in your area you might consider it. It's just like you, there is no one vaccine that protects you from everything. Each vaccine is very specific in what it does.
You need to vaccinate long enough before they are exposed to that specific disease so they can develop immunity. If they have never been exposed then older chickens can be successfully vaccinated, but that is easier right after they hatch. The longer you keep them the more likely they are to be exposed. The ideal situation if you vaccinate is if you hatch them with an incubator, immediately vaccinate them, and keep them in a brooder in your house for a few weeks. Exposure to other chickens or even the outside environment may introduce the disease.
I don't vaccinate mine but the only disease I know I have in my flock is Coccidiosis. I manage that by keeping the brooder dry and feeding them dirt from the run while they are in the brooder, starting at Day 2 or 3 and repeating twice a week. By keeping the brooder dry the numbers of the bug that cause Coccidiosis do not multiply to great numbers which allows the chicks to develop a natural immunity in two to three weeks without a vaccination. My brooder is in the coop with the adults so my chicks are going to be exposed anyway but feeding them dirt guarantees exposure.
I can't do that with chicks raised by a broody hen. One time when the weather set in wet for a long time chicks with a broody hen showed signs of Coccidiosis, that's how I know I have it in my flock.
I can't tell you what to do, you'll have to decide that on your own based on your conditions and experiences. Hopefully this helps you make an informed decision.
Good luck and welcome to the experience.