Colds are different from the flu (influenza). I had the flu two years ago and nearly had to be hospitalized. It lasted for a week and took two more weeks to recover from. People die from it all the time, which is why there is a recommended vaccine for people. I had never gotten the vaccine before I got sick with it, and let me tell you I am getting it annually now!
Common sniffles are usually a cold (or allergies), which is a different virus entirely...and yes, one that chickens don't get. I have just gotten over a cold (which actually ended up turning into bronchitis, so I was almost as sick as I was with the flu! I swear, my immune system...) which lasted for three weeks.
As far as I know, most of the outbreak of avian flu was confined to the commercial egg producers. I think I saw one small hatchery had been affected when I was looking around for chicks to order. So, pretty unlikely that the OP's chick have been exposed. I did feel the need to clarify that AI was a thing that existed though.