For whatever reasons I vividly remember asking the question in 7th grade, "can't a story not have a conflict? Can't it just be about some nice people getting along without anything like that happening?" and my teacher simply said "No."
When I learned 2nd person is indeed real I was pretty mad about that. Of course I should have already known it was real, reading Choose Your Own Adventure books, but I just didn't make the connection.
"There's no plot to speak of--things happen, and then it ends. There's no conflict to speak of until the last chapter. Most of the book consists of detailed descriptions of civil engineering projects and the magical techniques used for them. The characters are ludicrously overpowered special snowflakes. The language is nigh-impenetrable, and the innocent comma is tortured beyond all reason.
But you know what? To hell all that. I loved it.
This is a story about where legendary sorcerers come from. Five young people (ages range from late teens to early thirties) with magical talent take part in a highly experimental training program. Talent is hazardous; absent training, none of them are expected to live to see fifty. Traditional training, which runs along the lines of "spend several years sweeping floors and learning control before moving on to lighting candles", has a roughly fifty percent survival rate. Their program, in contrast, starts with completely reconstructing a square mile or so of geography and scales up rapidly from there."
It is, in fact, an extremely good story.
I also suggest Nathan Lowell's Solar Clipper series, a far-future space story in which nothing much happens and it is fascinating. Excitement is largely provided by superior coffee making and people management skills.
That's true about the first book, perhaps the second (is clothes shopping conflict?), but the third is completely different.
I also recall Robert Graves' writing, in 'Goodbye to All That', of one of his fellow soldiers saying that after the war, he would read the whole of Trollope's Barchester chronicles, as nothing happens in them, though that is not strictly true.
Had to google. Was delighted that I got to go to TV Tropes. http://tvtropes.org/pmwiki/pmwiki.php/Main/LampshadeHanging
Which certainly does allow for a conflict free story. The important thing is that a story has events which are causally related. Otherwise it really is just a list of unconnected statements.
By this logic, it seems that a recipe is a story. (Maybe that's intentional!)
I'd almost view the definition of a story as more about the intention than about the content—rather like art, which can (arguably) be created simply by the act of presenting it as such (in the sense of "found art" (https://en.wikipedia.org/wiki/Found_object )). So too, surely, can one have a "found story".
I don't disagree in general that stories can be conflict-free. But, good stories usually have character development, and character development almost always entails overcoming some internal conflict.