The alliteration sprinkled throughout the poem adds weight and emphasis to key words and lines.
For example, it adds a heavy sound to a number of phrases about slowness or difficulty: "I struggle / not to stray" (lines 5-6), "wheel on heavy wings" (line 16), and "I roamed through wreckage" (line 34). These alliterative moments seem to weigh down the lines, illustrating (respectively) the speaker's spiritual struggle, the slow and ominous flight of the "scavenger angels," and the speaker's sad wandering through the ruins of his life.
Alliteration can also draw thematic connections between the words it links. The alliteration between "tribe" and "true" in lines 17-19, for example, suggests that the speaker's "tribe" of loved ones was defined by "true" affection:
Oh, I have made myself a tribe
out of my true affections,
and my tribe is scattered!
The repeated /f/ sounds in "friends"/"fell"/"face" (lines 23-25) evoke the sharp, repetitive sting of "dust," while also linking the friends closely with their fallenness:
the manic dust of my friends,
those who fell along the way,
bitterly stings my face
For the grieving speaker, early death is something that's come to define the "friends [...] who fell."
Most notably, alliteration underscores the poem's central message: "Live in the layers, / not on the litter" (lines 37-38). Repeated /l/ sounds make this phrase especially resonant, affirming, and memorable. Interestingly, this phrase also alliterates with "lack" in the following line—perhaps the poet's way of slightly undermining the poem's affirmation. (Notice that there's a bit of anticlimax in lines 39-40 anyway, as the speaker claims not to understand the holy message he's just quoted.)