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. 

In the story "Chickamauga" by Ambrose Bierce, what is ironic about what frightens the boy?  

At the beginning of the short story "Chickamauga" by Ambrose Bierce, the little boy travels into the forest alone on an imaginary journey to vanquish his invisible foes using his mighty wooden sword. After crossing a shallow brook, the little boy advances from the bank of the creek, where he stands face-to-face with what Bierce describes as a "more formidable enemy," which ends up being a harmless rabbit. The rabbit frightens the boy, who quickly runs away and ends up falling asleep in a narrow space between two rocks.

As the boy sleeps, a violent battle takes place in the forest, and when he wakes up, the little boy sees hundreds of bloody, maimed soldiers crawling towards him. Instead of being frightened by the macabre scene, the boy finds the severely injured soldiers humorous and even attempts to ride on their backs as they crawl. Ironically, the harmless, innocent-looking rabbit scares the boy, but the grotesque soldiers crawling toward the brook do not frighten the little boy at all.

In the story "Chickamauga" by Ambrose Bierce, what is ironic about what frightens the boy?  

In Bierce's short story "Chickamauga," a young boy has frightening experiences as he walks through the woods. In particular, he encounters a group of soldiers who are bloody and injured as they come back from fighting. Surprisingly, the boy is not scared of these men. In fact, he climbs on the back of one of them as if they are playing. As the story progresses, he leads them forward like it is a game.

The things that do scare the boy are interesting. He startles at the sight of a rabbit and at one of the men when he raises his fist at the boy. The reader does not yet know that the boy is a deaf mute, so it is difficult to understand why he is afraid of a rabbit or a gesture, but not of bloodied soldiers. The irony of the boy's fear is that the thing that should scare him--the violence of war--does not.

It is not until the last scene, where the boy sees his mother murdered, that he shows appropriate, real fear. He finally realizes the dangers of war only when they strike something or someone he knows, namely his mother.