As others have noted, the stream-of-consciousness style Hemingway uses in "The Snows of Kilimanjaro" is associated with modernism. It's important to note, however, that stream-of-consciousness is not used by modernist writers simply as window dressing but comes from a deep desire to express their belief that knowledge is subjective, not objective. These writers, as Hemingway does, almost entirely dispense with the omniscient, all-knowing narrator because they didn't want to inject false certainty into their narratives. Instead, we see the action in the story in subjective terms as it is experienced by a dying man.
Hemingway also uses the spare, unembellished prose typical of the modernists, who wanted to get away from Victorian ornamentation.
In his treatment of a story about dying, Hemingway is strikingly modernist. Victorians loved sentimental and religious deathbed scenes, something modernists turned away from. Like a good modernist, Hemingway strips Harry's death of any false sentiment or religion. Religion is utterly missing from this story: after the shock of World War I's carnage, nobody is a believer. There is no praying, no invoking of angels, God, Jesus, or heaven. Harry's relationship with his wife is laced with fracture and bitterness, too, not sentimental deathbed reconciliation. He can be acidic as he speaks to her. They, for example, have the following dialogue:
“You bitch,” he said. “You rich bitch. That’s poetry. I’m full of poetry now. Rot and poetry. Rotten poetry.”
“Stop it. Harry, why do you have to turn into a devil now?”
“I don’t like to leave anything,” the man said. “I don’t like to leave things behind.”
In both style and content, Hemingway is doing something new, something that would have shocked earlier generations in its brutal honesty.
The stream-of-consciousness narrative technique is much in evidence in Hemingway's “The Snows of Kilimanjaro.” This technique was widely used by modernist writers as a way of giving the reader an insight into the subjective mental states of the characters depicted in their poems, novels, and short stories.
As is often the case in modernist works, the use of stream-of-consciousness in “The Snows of Kilimanjaro” highlights the sense of alienation from the world of a particular character. In this case, Harry is completely disillusioned with the world. He realizes that his life has been nothing but a sham, and resents the fact that his talent for writing has deserted him. Unable to spend his last remaining hours in the objective world, he retreats to the subjective realm, a world of fleeting thoughts and feelings captured by the stream-of-consciousness technique.
As he lies dying, Harry slips in and out of consciousness. But given his alienation from the world around him, a characteristic theme in modernist writing, the distinction between consciousness and unconsciousness becomes blurred to the extent that Harry loses his grip on reality. But then—in true modernist fashion—reality, as it existed in Harry's life, wasn't all that real to begin with.
Hemingway's story is modernist in the sense that the story of the man dying of gangrene in Africa is punctuated by "stream of consciousness"-like flashbacks to earlier moments in the protagonist's life, but also in terms of its theme which has to do with the fragmentation of the self—the desire to fashion some sort of wholeness out of his memory—and the horror of his war time experience, which has altered his view of life.
In particular, Harry is consumed with guilt over the "wasting" of his talent. The story is interrupted repeatedly by Harry's memories of Switzerland, Paris, and Turkey during the war, his time as a ranch hand. These memories he thinks of as so much literary capital—stories he could have written, but did not. Harry has instead squandered his life pursuing rich women. His constant fighting with his wife has little to do with her, or even the question of if he loves her; instead, it has more to do with the rottenness of life, which finds an ironic double in his rotting leg. The contrast between the vividness of his memory, his longing to have somehow written it all down, and the peculiar circumstances he finds himself in at the end of his life suggest the modernist attitude of the individual's alienation from society, or other people.
The most obvious reflections of Modernism in Hemingway's "The Snows of Kilimanjaro" are the first person narration and the "stream of consciousness" type sentences. Modernist writer's tended to write in the first person and favored stories told in clips and bursts of impressions rather than the typical beginning-middle-end type of story. Considering that modernist writers did not typically tell a story chronologically, Hemingway's use of flashbacks could also be seen as a modernistic technique. In the story's content, Harry's regret at not having achieved what he wanted in life could be seen as a reflection of modernism. Modernist writers often rejected social standards and in "The Snows of Kilimanjaro" Harry feels like he sold out when he thinks about his former days as a poor writer in Paris devoted to his craft and his present, comparatively, hedonistic lifestyle devoid of meaning.