It is helpful to think of genre categories as being somewhat flexible. A novel can be "literary", like Vonnegut's works, while also being science-fiction . Also, science-fiction works can and often do involve narrative elements that occur across many/all genres. This fact implies that science-fiction works draw from a...
It is helpful to think of genre categories as being somewhat flexible. A novel can be "literary", like Vonnegut's works, while also being science-fiction. Also, science-fiction works can and often do involve narrative elements that occur across many/all genres. This fact implies that science-fiction works draw from a larger body of authorial devices than any single genre can claim.
A specific analysis of Vonnegut's novel in light of your question will ask us to consider the various definitive characteristics of the science-fiction genre. The "future" is often the setting in science-fiction, but not always. However, technology is always part of a science-fiction story. Whether a story is set in contemporary times or the future, as long as it features a significant technological interest, the work can be categorized as science-fiction.
Another point to consider is that a book's publication date determines what, for that work, represents the future. If a work was published in 1965 and sets its story in 1990, we have to see 1990 as "the future".
Many Vonnegut works can be seen as science-fiction because they deal with issues of technology (and mankind's difficulties in showing restraint in using technology). As time-travel and inter-stellar space travel technology are both featured in Slaughterhouse-Five, this novel can be considered science-fiction.
However, Vonnegut's style is self-referential, meta-fictional, and postmodern in ways that might suggest we see his work as meta-science fiction. Ultimately, Vonnegut's work represents a tangential relation to "science-fiction proper" as it is not genre fiction but is instead more accurately seen as literary fiction.
Critics have focused on the novel's break from convention, in fact, which implies a separation between Vonnegut's work and genre fiction such as science-fiction.
In his 1990 study ‘‘Slaughterhouse-Five’’: Reforming the Novel and the World, Jerome Klinkowitz observed that the Tralfamadorian concept of time is also ‘‘the overthrow of nearly every Aristotelian convention that has contributed to the novel's form in English over the past three centuries.’