RaenaEnchant asked: Can flash fiction be individual stories in a series, using the same characters and setting?
ANSWER: Sure! Maybe.
It depends on whether each individual story in the series can stand alone as a story. If they can't, they're scenes in the larger story, not flash fiction.
If you want an example of an author who has done something similar quite successfully, look at Ray Bradbury's Dandelion Wine.
Dandelion Wine is a novel, but not quite a novel.
With Dandelion Wine, Bradbury strung a bunch of short stories together into a narrative that he cemented together with additional transitionary scenes. The result is a novel with a fairly thin plot--it has no more resolution than simply the end of the summer--but with some amazing stuff happening in the middle. Most of the 'chapters' in Dandelion Wine can stand alone as short stories, or can do so with only a very small amount of narrative removed.