The poem uses alliteration throughout. The first alliteration occurs in the first opening words of the poem:
My mother bore me in the southern wild,
The repeated use of the phrase throughout the poem shows the importance of the speaker's mother in shaping how the speaker sees the world. The alliteration has a gentle playfulness, convening the intimacy and affection between mother and son.
The rest of the stanza uses prominent /b/ alliteration:
And I am black, but O! my soul is white;
White as an angel is the English child:
But I am black as if bereav'd of light.
The alliteration associates dark skin with the state of being "bereav'd of light," building a sense that it is somehow inferior (or seen as inferior). Likewise with the link to the word "but," which is often a word that signals the introduction of a problem or obstacle (e.g., "I was going to go the shops, but they were closed"). Though the poem tries to suggest that race is irrelevant—at least in the afterlife—it is also subconsciously reinforces the idea that being Black represents a kind of flaw or fault.
This is picked up in line 15, where "black bodies" are portrayed as having "sun-burnt" faces, with the image of burning suggesting that something is wrong with black skin. The poem implies that this is because Black people are more adept at "bear[ing]" the "beams" of God's love, alluding to the heat and sun of the African continent. It's a somewhat confusing image because being "burnt" suggests that Black people do not really "bear" these rays effectively.
In line 18, the poem uses alliteration (and consonance) to suggest the presence of God's voice:
The cloud will vanish we shall hear his voice.
Notice how this cluster of alliteration seems to turn up the poetic volume of the poem (especially if read out loud), thus helping to create a sense of drama around the moment when God finally speaks to humankind.
After God speaks and invites humankind back into paradise (and/or heaven), the boys will live out joyful, carefree existences free from the limitations of earthly identity. Here the poem uses the alliterative simile "like lambs" to describe this eternal happiness and child-like innocence. The speaker imagines himself stroking his (divine) father's hair: "I'll send and stroke his silver hair[.]" This alliteration suggests intimacy and affection, and gently echos the use of alliteration to describe the other nurturing relationship in the poem—mother and son.