Whatever you decide to put into your First Aid kit for the chickens, I think it even more important to learn about what you can and cannot realistically expect to treat if a chicken falls ill or gets injuried. What you put into your head in terms of education is probably more important than the anything you might put into a First Aid kit. If you don't know how or when to use the supplies in your kit, then they have little value.
Many years ago I was a licensed EMT, and I carried an emergency kit in my car with supplies I had been trained to use. So that had value to me. I doubt if an average person could open up my kit and know what supplies were needed to treat a victim. When I became an RN, I learned many non emergency treatments, but they were almost all centered around care in a hospital.
My approach to my chickens has been to protect them as best I can from predation, and to give then a clean place to live. I make sure they have food and water available 24/7. I had 2 chickens die on me the end of last summer, and I still have no idea why they died. But I don't feel bad about it because I talked to a poultry breeder of 40+ years and with all his experience he told me that sometimes birds just find a way to die on you. My strategy is to replace older sick birds with healthy chicks. But my chickens are not pets, so I just look at the economics of the situation.
I think the best advice I have seen so far is to have a separate cage or carrier to remove a sick bird from the flock. If you treat it and it survives, that is great. If the bird dies, then at least maybe you got it out of the flock before others were infected. I have only once successfully treated a sick bird by removing it from the flock and giving it extra attention inside the house for a short period of time. But after it felt better, it went right back out to the flock. I have a pet carrier ready inside the garage for separating a bird from the flock if necessary.
Planning ahead is a great idea and I hope you build up a kit for most situations. Nobody wants to be running out to the store late at night trying to find supplies you should have, or could have, stocked up before the emergency.