The figure of speech used in the phrase "burly bureaucrat" is alliteration. Alliteration is a literary device in which a series of words in a sentence or phrase start with the same consonant sound. In this case, the repetition of the "b" sound in "burly bureaucrat" creates a musical and rhythmic effect. To identify this figure of speech, you can go through the phrase and look for any repeated consonant sounds at the beginning of the words.
