For such a short poem, Burns certainly packs a lot of literary devices. First, Burns uses a simile to compare his love to a flower--"Oh, my Luve's LIKE a red, red rose..." Secondly, his love is symbolized by that rose, and by repeating the color "red", he is how beautiful, how pure his love is. He uses another simile in the third line to once again compare his love to something beautiful; this time, he compares his love to a beautiful song--"My Luve's like a melodie..." Burns wrote in a lyric style, meaning this poem often reads like a song would--hence, the repetition of some key phrases. There is also obvious alliteration with the "r" sounds--"...a red, red rose..." The use of alliteration also furthers the sing-song musicality of the poem.
It sounds as if you are having some difficulty understanding the meaning of the term "literary devices." These are basically ways of organizing language beyond what is necessary to create meaning. Thus devices like meter, rhyme, repetition of sounds, figures of speech, and non-literal uses of words are all "literary devices." Literary critics usually divide these into "figures of sound" and "figures of thought."
In terms of sound, first you could look at meter. The poem consists of four-line stanzas, with the first and third lines written in iambic tetrameter and the second and fourth in iambic trimeter. The stanzas are rhymed ABCB. This scheme, known as "ballad meter," identifies the poem as belonging to the literary genre of the ballad. We also can see examples of alliteration, or repetition of consonant sounds in "red, red rose."
In terms of figures of thought, Burns uses "simile" or explicit comparison in the initial stanza when he compares the woman to a rose and to a melody. He also uses "hyperbole" or exaggeration in describing how much he loves his beloved.
Robert Burns also uses some hyperbole's such as when he mentions how he will love the mistress until all the seas go dry and how he would go to her even if there were ten miles inbetween them. The purpose of these are to show that the speaker would go as far as would for this girl and how his love for her is everlasting.