My initial reaction to this question is no.  "The Rocking Horse Winner", although very distant and flowing in its style, is not stream-of-consciousness.  In stream-of-consciousness writing, the writer goes wherever their brain takes them, and it usually involves longer tangents that go off in different directions before veering back to the main point.  It is more like the journey of one person's mind and all of their individual thoughts.  In this story, the narrator does not share his thoughts and journey but tells a story of a family, giving time to each character, and leading us along in a very specific direction. If you want to read a good example of some poetry that contains stream-of-consciousness writing in it, I recommend T.S. Eliot's "The Love Song of J. Alfred Prufrock" (I provided a link below).  In that poem he meanders about a bit, letting his mind's thoughts be shown as they travel; if you look at that poem, hopefully you can get a better feel for what stream-of-consciousness writing is.

In this story, there is a definite organization, purpose, direction, and focus.  It stays focused on telling the main story, and doesn't diverge on other subjects or tangents.  The style of it is that it is written more like a fairy-tale, so it sounds a bit magical, or "once-upon-a-time"-ish, but tells a story with a moral and lesson contained within it.  But every detail is focused on that moral and story, so it doesn't really fall under the stream-of-consciousness genre. 

I hope that answer and explanation help a bit; good luck!