People not uncommonly say that short stories are more like poetry than novels. Some short, single-focus stories may well be mistaken for poetry, just as some poetry gets called "chopped-up prose". In the journey from story to poem there used to be a no-man's land of unpublishable short prose. The only hope of publication for these pieces was in poetry magazines. Texts in the format of recipes or shopping lists became poems. Anecdotes and vignettes couldn't be prose-lineated in poetry magazines because they weren't "Prose Poems" - a term that had rather been taken over by surrealists and erstwhile experimentalists (Baudelaire, Russel Edson etc.) So they got a line-breaks make-over.
Now the literary landscape's changed - we have Flash. Flash isn't a genre or a mode. Definitions vary, but in practise it's short (less than 1000 words, sometimes a lot less) and doesn't use poetic line-breaks (though it may still use line-breaks the way that adverts, lists, etc use them). Usually it employs narrative, character or plot, but sometimes it uses juxtaposition. The style may be poetic without it needing to be a poem, though the more it jettisons traditional story features (character, plot, length) and adopts poetic ones (sound effects, form) the more like a poem it will be.
I think Flash writers reading some poetry magazines for the first time might see familiar material but might wonder about all the line-breaks - "It's Flash with hiccups". Some free verse writers don't like adjusting let alone removing line-breaks though they have trouble explaining what they are for - "they just feel right" ... "they just came out that way" ... "they give the imagery room to breathe", etc. The poets might indeed be able to point to a line-break that introduces a telling pause, neglecting to explain what the pauses presumably introduced by all the other line-breaks are for. The "free" in the phrase "free verse" means to me that the author's freed of the need to put line-breaks in just for the sake of a restrictive form, but that freedom has become a duty, with many poems adopting the regular rectangular stanzas of older formal poetry.
I don't think there's such a thing as a neutral line-break. They're never hidden characters. To me each line-break added is an effect that is potentially powerful but can as easily backfire. And yet, reading poetry one might believe that line-breaks don't have to pass stringent tests to justify their existence the way that adverbs do. Irrelevant ones are politely ignored, like someone's speech impediment. Take Catherine Smith's "Snakebite" (in the Forward book of poetry 2009). It's 13 3-line stanzas ending with "Tomorrow/ we'll feel sick as dogs. But tonight,/ here, under a bright, full moon,// we're amazing, and as we hug/ on my doorstep, I taste you,/ kiss the snakebite off your lips". If you gave a point for each line-break that did something and deducted a point for line-breaks that did nothing (or less than nothing), I don't think you'd come out with a positive score. It's not an auto-cue text, it's literature, so why not let the story speak for itself? "If in doubt, leave it out" is a maxim that can be applied to more than words. Flash takes the radical approach of eliminating the poetical line-break.
I think many poems written in the past few decades in retrospect fall more appropriately in the Flash category - poems like Carolyn Forche's The Colonel for example. Simon Armitage's poems in the Winter 2009 issue of "The Rialto" (a poetry magazine) looked very Flashy to me. Some magazines ("Tears in the Fence", for example) avoid genre classification by not labelling sections "Prose" and "Poetry". Sometimes (as in a few New Writing anthologies by the British Council) there's a section entitled "Texts" for debatable works.
The 2 Flash writers I've followed most closely (it's hard to avoid them if you read online) are Vanessa Gebbie and Tania Hershman. They both write poetry and short stories as well as Flash. Their Flash spans a spectrum. Pieces like Tania Hershman's "Hand" is where poetry takes over from Flash. The shortest piece in her The White Road and Other Stories book (Orange Prize Commended) is 102 words long. She's got Flash into the august "London Magazine", and in June 2010 BBC Radio 4 will present a week of her Flash. Vanessa Gebbie's contributed to "Field Guide to Flash Fiction" (Rose Metal Press), and has edited SHORT CIRCUIT - A Guide to the Art of the Short Story. Her Flash tends to be closer to prose, I think, which may be because she's more serious about her poetry (her work's been short-listed in the Bridport poetry competition).
Both are relatively new writers emerging without historical baggage into a world where Flash is a viable option and poetry isn't necessarily considered a higher form of art. It will be interesting to see how this new generation of writers redefines the genres.