Alliteration is used here and there throughout "Thirteen Ways of Looking at a Blackbird." It's an important part of section three, for example:
The blackbird whirled in the autumn winds.
It was a small part of the pantomime.
The two /w/ sounds in line 7 convey the power of the autumn winds. The two /p/ sounds represent the blackbird's interconnected place in nature, the alliteration drawing its own connection between the line.
There isn't a huge amount of obvious alliteration elsewhere in the poem, but there is some in section five between the two mentions of "beauty" in lines 14 and 15 and the word "blackbird" itself. These /b/ sounds could be seen as a kind of ornamentation, evoking the idea of beauty (which is tied to perspective—beauty is in the eye of the beholder).
Another key example is in section nine:
When the blackbird flew out of sight,
It marked the edge
Of one of many circles.
This section is about different perspectives too, describing the point at which a flying blackbird can no longer be seen. The speaker imagines "many circles" of perception, and how the blackbird's flight "mark[s]" the edge of the speaker's own field of vision (perception). The two /m/ sounds are like marks on the page, mimicking the way the blackbird's black shape in the sky marks the edge of perception.
Finally, there is alliteration (specifically sibilance) in the final section of the poem, with "snowing," "snow," "sat," and "cedar." These quiet sounds bring the poem to a calm close, reflecting the quietness of the scene at hand: a bird sitting on a tree limb, surrounded by snow.