As far as figures of speech, Burns's poem is chock full of similes, which is when a writer makes comparisons of two unlike things using the words "like" or "as." For example, the speaker of the poem proclaims: "O My luve's like a red red rose that's newly sprung in June." He is comparing his love to a newly sprung red rose, perhaps alluding to a new love in his life, one that has recently sprung up. The reference to June is also significant, as many writers use seasonal symbolism. Spring is the season of new birth, of new love, etc.
Another simile Burns employs is: "As fair thou art, my bonnie lass, so deep in love am I." He is comparing how much he loves her to how beautiful ("fair") she is.
Enjoy analyzing this love poem and looking for further examples of figurative language!