Stream-of-consciousness is a narrative perspective created and used by Modernist authors such as Joyce, Woolf and Mansfield. It involves trying to depict accurately the way that the mind jumps around from one idea to the next with free association. Stream-of-consciousness is therefore identified through the way that it tracks the thoughts and feelings of one individual character. It can be quite hard to read as it seems to have no logical structure, just like the thoughts of humans.
However, arguably "Barn Burning" does not use this narrative approach. Faulkner certainly tells his tale from the perspective of the young Sarty and tries to structure the narrative consciously so that, on the whole, the story is told from his point of view and the reader is presented with his view of events. However, the narrative is too structured and there is very little free flowing of thoughts as would be expected if the point of view was stream-of-consciousness. Note how Sarty is introduced in this quote from the opening paragraph:
The boy, crouched on his nail keg at the back of the crowded room, knew he smelled cheese, and more: from where he sat he could see the ranked shelves close-packed with the solid, squat, dynamic shapes of tin cans whose labels his stomach read, not from the lettering which meant nothing to his mind but from the scarlet devils and the silver curve of fish...
Sarty's point of view is presented accurately as he is unable to read and therefore can only make out the contents of the tins through the pictures that adorn them. However, there is no indication of free flowing thought in the way that a reader would expect. Faulkner keeps the perspective focused throughout on a boy who is struggling to know how to cope with his father and what his father has done.