As I've been focused almost exclusively on Flash for that past couple of years, I'll cut and past my response to a question about 'micro' fiction at another forum:
Yes, it(Flash/Micro fiction) should be a 'complete' story. One way to think of it is perhaps like a poem. A poem is complete on it's own and most are less that 100 words.
That said, there are many ways to tell such stories. The main thing you want to do is compress, compress, compress without losing any of the emotion. If it is done well it can tell a story as well as a novel.
Micro of course is a significant step beyond flash (typically 1000 or less).
I'm gonna throw out a couple of titles. The best guide to writing flash (not necessarily micro) IMO is the
Rose Metal Guide to Flash Fiction which includes instruction, examples(some of best published flash) and prompts... in the same vein is the
Rose Metal Guide to Prose Poetry.
If you really want to write these short forms they are invaluable.
A couple of suggested readings/anthologies/collections
Flash Fiction
Flash Fiction International
Lydia Davis writes some very short stories - some as little as one line. Her collected stories and Can't and Won't are both great!
Stuart Dybek is just simply amazing! Coast of Chicago and Ecstatic Cahoots!
Prose Poet
David Shumate was the inspiration for my most recent collection.
Here's a piece in The Guardian I just found by Googling:
http://www.theguardian.com/books/201...-flash-fiction
There is a good article here from one of the well knows flash fiction editors:
http://www.worldliteraturetoday.org/...d#.VVoWjflVhBd
I'll shut up now, but I could talk for days about this topic.