Hemingway's simple, journalistic style does not allow for much alliteration or flowery prose.  He's a straight shooter, and his narrative voice offers little prosody.

Here are a few examples:

• "His choice had been to stay in the deep dark water far out beyond all snares and traps and treacheries."
• “I’ll kill him though,” he said. “In all his greatness and his glory.”
• “I must hold his pain where it is, he thought. Mine does not matter."
• “But man is not made for defeat...A man can be destroyed but not defeated.”

As you can tell, these examples of alliteration are usually coordinated at the end of sentences to serve as a flourish.  Usually, there's "and" or other filler words in between so that the alliteration is broken up slightly.  In all, Hemingway uses alliteration sparingly so as to keep the narrative grounded in the way fishermen talk.