There are two definite occurrences in which Ambrose Bierce uses situational irony in his short story, "Chickamauga."
Situational irony is defined as a literary device in which what is expected to happen is the opposite of what actually happens.
In this story, the little boy is first frightened by a rabbit.
"Advancing from the bank of the creek he suddenly found himself confronted with a new and more formidable enemy: in the path that he was following, sat, bolt upright, with ears erect and paws suspended before it, a rabbit! With a startled cry the child turned and fled, he knew not in what direction, calling with inarticulate cries for his mother, weeping, stumbling, his tender skin cruelly torn by brambles, his little heart beating hard with terror--breathless, blind with tears--lost in the forest!"
It is ironic that something as harmless as a rabbit, which is an animal of prey and not a predator, frightens the little boy to the point that he runs so far as to become lost in the forest.
The second instance of situational irony occurs when the boy encounters the soldiers returning from a battle. It is ironic that he is not frightened of these bloodied men at all. The men are crawling on their hands and knees, and many are maimed. The little boy interprets their bloody wounds as the paint he has seen clowns wear. He interprets their crawling as a game and attempts to ride on of the soldiers like he rides his father's "negroes" at his home.
"He now approached one of these crawling figures from behind and with an agile movement mounted it astride. The man sank upon his breast, recovered, flung the small boy fiercely to the ground as an unbroken colt might have done, 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 unnatural prominence of nose, the absence of chin, the fierce eyes, gave this man the appearance of a great bird of prey crimsoned in throat and breast by the blood of its quarry. The man rose to his knees, the child to his feet. The man shook his fist at the child; the child, terrified at last, ran to a tree near by, got upon the farther side of it and took a more serious view of the situation."
The boy has no framework for understanding the appearance of the man without a jaw. He can see the fury in his eyes, but it is only when he shakes his fist at him that the boy becomes truly terrified. It is ironic that the entire entourage of hundreds of wounded soldiers did not phase him, but the anger of this one terrifies him.
There is another incidence of irony at the end of the story when the author reveals that the child is a deaf mute. This explains why he hasn't heard the sounds of battle, and therefore hasn't interpreted it as such.