This poem deals with a kind of immortality, really. In his speculation about entering into "English heaven," the speaker alternately comforts the reader (in case they were going to grieve for his death) and subtly reassures himself of his rewards in heaven, should he be unfortunate enough to be killed in the war back here on Earth.
To that end, this poem's use of sound emphasizes that kind of cosmic continuation (returning to England in heaven, even after death) by using a ton of repetition throughout. Just like the speaker will return to England in the afterlife, we get a lot of sounds, and words, that return to us in this poem. What's that? You want proof? You can't handle the proof! Oh, sorry about that. We got carried away there for a sec. Here's some proof for you:
First up, we have alliteration, the repeated beginning sounds of words, going off all over the place here. In lines 2 and 3, we have the repeated F sound: "foreign field" and "forever." Then in lines 7 and 8, we have the B sounds: "bodies," "breathing," "by," and "blest by." Line 12 gives us "sights and sounds," line 13 has "laughter, learnt," and line 14 ends with "hearts" and "heaven." But it's not just the beginning sounds that are repeated here. Even in a very short poem like this, we have full-on words that get repeated, like "dust" (lines 4 and 5), "rich" or "richer" (4), and of course the big one: "England" or "English" (six times in just 14 lines!).
So what are all these repeated sounds doing in the poem? If you consider that the speaker is essentially imagining how, if he dies and goes to heaven, he'll get to repeat his happiest experiences from home all over again, then this strategy starts to make sense. It's interesting to note that the speaker isn't dead yet (it's hard to write poetry when you're dead, after all), but the use of sound in the poem seems to suggest the same sorts of repetition he expects if and when he does reach the pearly gates.