What is the significance of time-travel in Slaughterhouse-Five?

Time-travel works on at least two levels or toward two purposes in this novel.

1. Time-travel is a thematic element of the novel, relating to notions of fragmented self/identity and to the persistence of memory as it emerges (uncontrollably) in the present. Billy cannot remain in one moment just as the narrator/Vonnegut character is drawn to re-live the past while living in the "present". Both these figures are challenged to integrate their psychological experience with/in the present moment and are subject to the powerful continuing influence of traumatic experiences from the past.

The following line is applied to Kilgore Trout in the novel but also describes the relationship between Vonnegut and Billy Pilgrim: 

‘‘He and Billy were dealing with similar crises in similar ways. They had both found life meaningless, partly because of what they had seen in the war.’’

2. Time-travel forms the logical backdrop of the fragmented narrative structure of the novel. The tapestry-style and discontinuous narrative structure offer a view of story-telling that is Postmodern, compromised and unstable. 

 In this way, the novel's structure highlights both the centrality of Billy's war experiences to his life, as well as the profound dislocation and alienation he feels after the war. (eNotes)