You have asked for help to begin an analysis of a Civil War short story by Ambrose Bierce. One of his more familiar stories is "Chickamauga," as referenced in your question, and there are several avenues available for you to consider as you begin to formulate an argumentative thesis and essay.
A good place to start is to ask the question "why" of an author or a piece of literature. For example, you might think about why Ambrose Bierce uses a young child ("a boy aged about six years") as the main or focal character in a story that is otherwise about war. What message did Bierce mean to send to his readers about the contrast between the innocence of the child and the harsh reality and depravity of warfare?
Or you might consider why Bierce left until the very last few lines the fact that the boy is a "deaf-mute," which seems like a fascinating descriptor of a character that a reader might have wanted to know earlier in the story. What did waiting until almost the very end of the story do to emphasize that revelation? Why was the story possibly made more powerful when told from the perspective of a child who could neither speak nor hear than it might have been told from the perspective of a child who could both speak and hear?
You might ask why the boy seemed to find himself more frightened of "the superior forces of nature" (such as the rabbit he encounters, and the fire at the end of the tale) than by the bloody, dying men crawling out of the woods toward the water. What do you think Bierce wanted the reader to think about when he/she read that the child was terrified of a rabbit but amused and even delighted with the dying men? What message does that send readers about the naivete of children, or the horrors of war, or how war makes equals out of adult and child alike, or how war seems to turn everything in the world, everything you thought you knew to be true, on its head?
You might ask whether (another version of a "why" question) the story would have been better if one of the dying men had told it. If so, why? If not, why not? How does Bierce call attention to the difference between a civilian's point of view (the child) and a soldier's point of view by using just the child to narrate (for example, what does the child notice in the story as he plays through the woods with his sword against an imaginary foe; what do the bloodied soldiers seem so intent upon gaining)?
Good luck with your position paper!