Stream of Consciousness is a literary device, but the phrase, or something like it, was used by the psychologist-philosopher William James in this Principles of Psychology to describe states of consciousness, or thoughts or ideas, as being a process, a flow, rather than isolated and distinct from one another. Efforts were made by certain authors to replicate this flow in their poetry and novels. Famous practitioners were James Joyce, William Faulkner, Jack Kerouac, Virginia Woolf and others.
I doubt that the literary technique is or can be anything like the process or flow conceived of by James, however. The fact that it's employed for a purpose--that it is indeed a technique, a contrivance--renders this impossible. What James and others (like John Dewey) point out is that typically our states of mind or consciousness are non-reflective. In other words, we don't constantly think; we don't consider means and ends, we don't anticipate events or consequences. In fact, we seldom do. We think when we have to do so, or are induced to think by encountering a situation we find problematic or dissatisfying in some sense. Then, we seek to resolve it. For the most part, we merely feel, or react thoughtlessly, as a "habit" to use Dewey's terminology.
Stream of consciousness writing is deliberate, and requires thought. Through thinking, the practitioners of Stream of Consciousness writing attempt to imitate that which isn't thought.
It doesn't work. If you read examples of it you may find on the internet, I think you'll agree with me. What you'll see, I believe, is an effort to express thoughts or feelings in an unconventional manner, sometimes disjointed, sometimes juxtaposition is unexpected, sometimes surprising but not as a stream or flow. In fact, the thoughts, feelings, ideas presented using the Stream of Consciousness technique are staccato.
How could they not be? It's a limitation imposed by language itself, I think. Even shorn of such words as pronouns, the description of walking in the woods would be something like: Walking, exercise, wood smell, sunny, feeling fit, warm, getting tired, etc. The description is necessarily made up of separate items, independent of one another.
Words, books, poetry, fiction and non-fiction prose aren't part of James' stream of consciousness, because they're read. A book or books might be when we merely see or encounter them, but reading and understanding them are not.
It's true that they may serve to evoke a feeling, however. But that feeling, having been evoked by the effort of reading and comprehending, isn't part of the stream. Like reading itself, like thinking, like acting for a purpose, they can be thought of as islands in the stream of consciousness as my old friend put it. They break up the stream, they divert it, for a time. Then, we get back to simply existing.
Because writing supposed to reflect a Stream of Consciousness clearly does no such thing (or so I think) I wonder whether such writing was more a fad than anything else. Perhaps Gertrude Stein was reading James on psychology on day and was struck by the idea, and passed it on to her acolytes, who passed it on in turn. E.E. Cummings is said to be a poet who used the technique. If so, his poems always strike me as disjointed, deliberately so--staccato, in fact--and perhaps that can be said to prove my point. His poems have impact, but they can hardly be said to flow. They don't flow, they jerk from point to point. It seems odd to me that any writer would think that they were accurately portraying the way our consciousness works using this device.
Ultimately, perhaps, reading prompts us to decide what kind of island in the Stream of Consciousness writing we want to live on or explore, for a time. The part of the writer is to make the island worth exploring. What is worth exploring will vary from person to person and time to time, of course, but that's the way of real islands as well.