I’ve read stories, some by my favorite authors, that had little or no dialogue in them (and they were excellent stories). I’ve written a few stories myself with little or no dialogue in them; but dialogue is one of the most powerful literary devices that the flash fiction writer (or any writer) has in his or her toolbox.
Dialogue engages your reader’s imagination probably better than any other device a writer can use for immediacy. Your reader “hears” your characters. There is nothing like dialogue to make your characters seem like they are actually “alive.”
Now this short blog post cannot teach you how to write dialogue. I suggest that you consciously “listen” to how people talk. Then you have to read authors who are known for writing good dialogue (for me it was Hemingway, John O’Hara, F. Scott Fitzgerald and Raymond Carver) and then you have to get over your fear of writing dialogue.
Just remember this. Dialogue is not just “talk.” Dialogue should move the narrative efficiently toward its resolution. Dialogue should characterize the speaker. And the best dialogue resonances with the themes and the point of what the story is really all about. This is especially important for the flash fiction writer because so much of a flash fiction story must be implied.