Without knowing which respiratory thing it is, whether it's viral or bacterial, the only thing you can do with the exception of vetenary help is to treat with antibiotics. The type that goes into the water, available at farm/feed stores. There is an egg withdrawal with that, for the duration of use. 10 days for treatment.
If it returns after treatment, it was viral, or something in their environment. Antibiotics will mask the symptoms but will not kill the virus. If it does not return, it was bacterial and the antibiotics did their job. Treat the whole flock, so that they are not swapping it back and forth to each other. Disinfect all drinkers and supplies regularly. Don't let poo build up. Keep things clean, and dry.
If the coop area is especially dusty, you'll want to get that under control as well. Switch bedding types if needed.
Chickens are still birds, and birds are really sensitive. Dust, high humidity, common bacterial infections and the like.. runny noses could be about anything. The first sign of something serious, or a reaction to their environment. Cedar shavings would set them off as well, as it's really harmful to the respiratory tracts of birds and other animals.
Luckily antibiotics have cleared up any runny noses I've encountered. Haven't had anything more serious than that so far. I hope the same for you!
