I jumped right in with The Other Side of the Window, by Tony Wassom. A recent widow lingers over breakfast, in a definitely melancholy frame of mind. Why? What is she going to do? You find out fast in a thousand word story!
Because the stories are so brief, I immediately read the previous day's offering, Ruby, by Virginia Pye. This story is from a dog's point of view, and it works. Very clever.
The fun of flash fiction is that the author can experiment with characters, literary devices, and themes he or she may be reluctant to pursue for a longer story, or an entire novel.
On a slightly different topic, if you like a little laughter with your mystery, here's an article by author Peter DiChellis on A Funny Thing Happened on the Way to the Murder. Learn why humor works in a genre focused on crime.