First of all, let me say that this is a particularly difficult assignment. It assumes, by nature, that you have read both Unbroken and To Kill a Mockingbird and have an understanding of these two characters to such a depth that you can roll-play one of them in a letter to the other.
The character called "Bird" in Unbroken is Corp. Mutsuhiro Watanabe, the Japanese sergeant who tortured (but tried not to kill) POW's at Omori, a camp on an island in Tokyo Bay. To be honest, the Bird is one of the most disturbing characters I have ever encountered in a story. He is described as a pathologically brutal sadist. Even the other Japanese soldiers didn't like him in the camp because he was "too violent." He took a sick and very twisted (almost sexual) pleasure in torturing the prisoners, and preyed on those (like Zamperini) who seemed unbreakable, the most.
I cannot even begin to give you advice on how to write from such a character's perspective, because this man's actions and attitude were portrayed as inhuman. I think if I had to write this assignment, I might assume the perspective of the Bird long after the war was over, and try to portray what his mindset might have become in light of the war ending, but also the details of POW camps being written about and exposed. (According to a CBS "48 Hours" special, the Bird is still alive and has defended his brutality in interviews, claiming he believed his actions were justified in light of the fact that the Americans were enemies of the Japanese during the war.)
In the way of ideas, I'm not sure what kind of knowledge or wisdom a character like the Bird could have to offer a character like Scout, but perhaps you could write his letter as a confession of sorts, or a revelation of the mind of a character who was so feared by prisoners, and now so hated by readers of Hillenbrand's book. Maybe he could testify to the kind of characteristics a person would need in order to survive a POW camp (as certainly, he would have seen what kind of character lived through torture). Good luck with this. Again, it sounds like a very difficult assignment.