Certainly, in one sense, every piece of literature is a reflection of its author, as you can hardly write about something convincingly that you have not lived, to a certain extent, yourself. However, it is true that Hemmingway's fiction in particular reflects his life and in particular in this story we can see how Harry could be identified with the author, both in terms of his many women and the bohemian wanderings that are true to Hemmingway's life. In particular, perhaps we can find an interesting parallel through the theme of writing and art.
Hemmingway himself struggled with his writing and the success that he wished he could attain and we can see that Harry's failure to achieve the artistic renown that he hoped for in life is one key theme of this story. The flashbacks that plague Harry as he dies depict a very Hemmingway-esque Harry in his former years, devoting his life to writing and living in Paris. His decision to leave that time of artistic purity is one he deeply regrets, and he feels that his subsequent pursuit of rich women and hedonistic pleasures has compromised his artistic talent.
It is important to notice how Hemmingway establishes a direct connection between the gangrene that is killing him and his perceived failure. Note how Harry says "Rot and poetry. Rotten poetry." In spite of the way he has let his talent languish, ironically it is at the moment of his death when we see his creative talent return strongly as he imagines a beautiful, haunting scene of salvation and being lifted up to the snows of Kilimanjaro. This transcendent ending perhaps shows the triumph of artistic talent that shows itself to be superior to death.
Thus we can establish many parallels between the character of Harry and the author, though of course we can only take those parallels so far.