The figure of speech used in the phrase "burly bureaucrat" is called alliteration. Alliteration is a literary device where a series of words in a sentence or phrase have the same sound at the beginning, creating a rhythmic effect. In this case, the repeated 'b' sound in "burly bureaucrat" contributes to the alliteration. To identify the figure of speech, one must recognize the repeated consonant sound and understand its effect on the overall impact of the phrase.