I’ve done both. I used to play in the Challenges a lot, and I’d do a lot of flash fic one shots in response to those (which reminds me that I need to update the links to those, dammit). I also did multi-chaptered stories comprised of flash-fic chapters. That was actually sort of insane but fun. And of course, I did a four-part short story series for the Holiday prompts, only because the setting I created wouldn’t leave me alone.
So honestly, I’d say to do it the way that feels most comfortable to you as the author. If you like the pieces as individual one shots, that’s how you publish them. If you feel they work better as a multi-chaptered work, that’s what you do.