I'd attach a picture of the chair and email production of Chicago Fire to see if they can confirm the story. It seems that the guy is an honest person and his story is quite elaborate and detailed, but I've been wrong before.
I don't know the signatures at all. I've actually never heard of the show, but I figured I'd add my input anyways. All the help the better :).
he did say he has an email saying that he had won that item in a raffle from production and were he could pick it up and will given winner a copy of that.