To see if Trout Fishing in America would be considered a postmodernist text, let's take a look at both contexts.
Postmodernism is a literary, theoretical, and artistic movement broadly encompassing the late twentieth century. The themes related to postmodernism are irony, critique, anti-universalism, and a rejection of totalizing theories and meta-narratives. Postmodernism was largely popular during the 1940s–1970s. To see if a work is considered "postmodernist," one should take into account the time and context in which it was written or produced and how its content relates to postmodernist themes.
Trout Fishing in America is an experimental 1967 novel by Richard Brautigan, a writer and poet from San Francisco. The literary movements that were popular in 1967 in San Francisco include postmodernism, beat poetry, surrealism, and absurdism, among others. In terms of content, Trout Fishing in America does not have a linear plot structure and is darkly humorous and at times absurd, with the phrase "trout fishing in America" taking on different meanings throughout the novel. It does use irony and reject the meta-narrative (or in this case, just a narrative) that is popular in fiction writing. Therefore, because of the time it is written and the content of the book, Trout Fishing in America could be considered a postmodernist text, though its themes fit better with the literary movement of absurdism.