Several years ago I had a Quail contract WEE, Western Equine Encephalitis, similar in symptoms to West Nile and carried in the same fashion with mosquitoes. Let me tell you, it is NOT a pretty sight to watch a bird go thru this disease. They can have reoccurring symptoms years later and causes tremors, pancreatitis, lameness and a basic long winded illness.
Anyway, I spent months and months doing research on West Nile, WEE and EEE in attempt to ease this birds pains. HOWEVER, I did come across a web site on Chickens and West Nile Virus. From what I understand, only certain species of birds are suseptable to West Nile Virus, and Chickens are not one of them. Supposedly, after a Chicken is bitten by a mosquito with West Nile Virus, they develop antibodies to the virus within 4 days of being bitten. While other highly suseptable birds such as quail, will incubate the virus for 10 days and either combat it with their immune system or get full blown West Nile Virus.
But a long story short, generally, healthy Chickens will throw it off with their immune systems and you will never know they have been bitten by a mosquito with West Nile.