Free contest? Isn’t that an oxymoron? Not when we’re talking about Press 53/Prime Number Magazine’s 53-word story contest. It happens monthly based on a prompt. It’s free to enter. Check it out here: 53-word Story contest.
Then there’s the Flash Fiction contest, which isn’t quite free. ($7 to enter, $251 prize.) That one is also monthly. Check out the rules here: Flash Fiction Contest.
Press 53 also has a big contest, the Press 53 Award for Short Fiction, which awards a prize of $1500 (advance on royalties) for a short story collection. This one is annual, deadline December 31: Press 53 Award for Short Fiction.