I’ve had termites in the house. What a pain. They can do some serious damage but at least you should not have the Formosa like on the Gulf Coast. Those things don’t take long to be real destructive.
You can always hire a professional to treat them. They should know what can or cannot be used around chickens or other animals. They should. But some are more professional than others. I’d want to chat with them enough to satisfy myself they really understand about the animals like chickens.
In your situation I’d probably call my extension agent, in the phone book under county government or fine contact information online. The agent probably won’t know personally but they should line you up with someone who does. That someone will probably be associated with your land grant university, maybe a professor. I think in North Carolina you may have more than one land grant university.
They should be able to tell you how to treat the termites and what you need to do about the chickens. Since a chicken’s respiratory system is really delicate I’d want to know about any special precautions for that. I’d also ask if there is any withdrawal period before you can eat the eggs or butcher them.
Good luck. Those things aren’t any fun.