I'm not sure that death is really analyzed in "Chickamauga." It's more presented. An analysis would imply that there is some discussion of death as a concept, or that the reader might come away from the story with a greater understanding of it, but that isn't the case. The scene is presented to the reader via the perceptions of the child and the author leaves the conclusions up to the individual.
The point of the story would seem to be the contrasting of the boy's heroic visions of warfare with the realities he comes across following the battle of Chickamauga. Death is presented in the story without much sugar coating:
...then turned upon him a face that lacked a lower jaw—from the upper teeth to the throat was a great red gap fringed with hanging shreds of flesh and splinters of bone.
The wounded men "crept like babes." They writhe and squirm. Some of them, making it to the creek, drink from it and then can't lift their heads back out. Death is presented as being a process going on everywhere, gruesome and horrific.
Of course, to the child, he cannot understand what he is seeing. He has no real concept of death, only of fear. It is only when he finds his home again, in flames, and finds his dead mother that the idea seems to hit home.
Overall, death is shown in the story as being a horrible process. Soldiers and civilians alike share it. Though for some it is instantanious, for many it is a grim period of waiting. Despite the boy's enthusiasm, the results of warfare are anything but glorious.