Let us remember that alliteration is defined as the repetition of initial consonnant sounds in a series of words that are together or at least close together to produce a particular sound effect in the poem and help it to "flow" better. Alliteration is a technique that Byron uses a lot in this poem, and there is an excellent example in the first stanza:
The Assyrian came down like the wolf on the fold,
And his cohorts were gleaming in purple and gold;
And the sheen of their spears was like stars on the sea,
When the blue wave rolls nightly on deep Galilee.
Note the third line and the repetition of the "s" sound in words such as "spears," "stars" and "sea." Note how this alliteration, with the simile that is built around it, serves to emphasise the might and power of the Assyrian force. They are so numerous that the sheen of their spears appear to be like many different stars. Byron is exaggerating their numbers to, in turn, highlight the power of God in destroying them later on in the poem.