While I love my chickens dearly, my birds are not pets. I want a healthy, vigorous flock that provide eggs and meat. So for me it would depend on the emergency. For mild injuries I might just separate the bird from the rest of the flock for a few days so it didn't get picked on while it recovered. Seriously injured birds requiring extensive rehab would be loved up, apologized to, and then converted into chicken and dumplings, assuming the injuries had not contaminated the meat. Visibly ill birds would be culled for protection of the flock. So what I keep on hand is a cage for isolating a mildly injured bird, a sharp knife, and a stew pot.
If you insist on a medical kit for emergencies, vet wrap is essential. It's a staple in my human emergency kit. Much cheaper than the nearly identical "athletic wrap" or "bandage wrap" you can find at the drug store. And it comes in better colors. Plus you can use small strips of it as temporary leg bands to mark chicks. Great stuff!