This is a tougher one to answer and you might get some different perspectives from other people. There's definitely some subjectivity to it. Personally speaking, I put a lot of weight into "completeness" of the story. The more that it tells and the better image it puts in the reader's head, the better. But it can't feel unfinished or rushed either, so it all has to fit together really well. It also can't feel unsatisfying.
I believe it's fine to have some elements that are open to interpretation. Sort of like a painting. People can have opposing views on what a painting means, while also liking it just as much as the other person they're in disagreement with. The important thing is: that no matter what meaning the reader gets out of your story, that it's an interesting and satisfying one. Since it's writing though, you still want some cohesion that makes the story. You're just leaving more things up to the reader's imagination.
Due to the format, the imagery can't always come from longer and detailed descriptions, but instead more from subtle additions. If you can write a sentence that accomplishes an action, develops the character or situation, and gives insight into the surrounding world all at the same time, then that'll add a lot of value to the story. That doesn't mean you can't devote sentences to individual tasks, but you'll want to try layering plenty of content together. Every sentence needs to have some kind of significance.
For example:
The shabby Balinese cat meowed dejectedly, as Matt came limping home late again covered in silt and blood
That's 18 words and accomplishes a number of things:
-Shows that Matt has a cat.
-Matt also has a "home" somewhere.
-Matt was doing something all day.
-Late can have two meanings here: it either means later than usual, implying in the past he arrived earlier in the day. Or it can simply mean it's nighttime and maybe he always arrives at night. This can be left to reader interpretation or clarified elsewhere in the story.
-This is not the first time Matt has returned late recently, whichever of the above meanings it is.
-The cat is a long-hair breed (Balinese), which requires a lot of extra care compared to most short-hair breeds. Since it's described as shabby, Matt hasn't been taking very good care of it recently.
-This is further emphasized by the cat's dejected meow, showing it may be unhappy and/or depressed.
-The cat's not dead and hasn't run away, so clearly he's feeding it still.
-To feed the cat means he has to get cat food from somewhere, whether it's a job or stealing it.
-The cat meowing can also imply that he's had the cat for a while and it appreciates him to some degree, enough so that it still goes out of its way to meow instead of acting indifferent upon another late return. If it didn't like him at all, it wouldn't still be living in his home.
-Matt limping and having blood on him shows he's been injured in some way. Or he could have had the limp already and the blood is from something else.
-Matt having silt on him can imply a number of things. Maybe Matt is a chimney sweep. Or maybe he doesn't have a job at all and simply can't afford to clean his clothes.
That sentence can also create some questions for the reader, to (hopefully) help hook in their interest: Why is he covered in both silt and blood? Is he hurting people? Are people hurting him? Is this in connection with a job or is it happening elsewhere? Is he not injured enough to need to see a doctor? Or maybe he can't afford a doctor even if he needs one, considering he's limping and already having trouble simply taking care of his cat? Or maybe he's had a limp all of his life?
While there's some open-endedness, there's also some fairly concrete details that all readers will get regardless of how they view the sentence. You use those clearer aspects to help bind together the important elements and to tell the story, while leaving the less clear things to their imagination to further build upon what's there.
With that example sentence, you could even add an extra sense like sound or smell, to add some description of his home. Or that could be hinted at elsewhere in some other way, or skipped altogether if it's not important to the overall direction of the story. While in a full story you can expand on a lot of the little details, part of flash fiction is leaving some of it up to the reader's imagination. Or even better, being able to heavily imply things without directly needing to say or explain them. Again, it's about trying to accomplish more with as few words as possible.
Some other factors being writing style and variability of descriptive of words. Since you're working with very few words, if you lean too much on certain ones or even repeat yourself, it starts to stick out and can take away from the flow of the story. A creative descriptive word can also really change or enhance the meaning of a single line.
For writing style, we all have our own ways of approaching our storytelling and some of that is personal preference. Other times, people (like myself) are sometimes challenged with bringing life to their words. You can know the story you want to tell and it could be really interesting, but if the words feel empty and not vivid enough, then the reader won't connect with it. Good flow is especially important for flash fiction, since you don't want the reader to trip over poor wording or become disinterested. This loops back to density being a factor. Everything good or bad about a story is multiplied when writing something this short.
Even though I say the story should be "complete", that doesn't mean it actually has to tell the entire story that's happened. It just needs to feel like a complete and concise experience that's enjoyable front-to-back, which can also hint at a larger story without actually telling it directly. In fact, good flash fiction can leave a great untold story to the imagination of the reader. Some people even outline a full story and simply write a scene from the middle of it. Also, your first sentence and last sentence are really important. The first to hook in the reader. The last to tie everything together, create some closure, and hopefully make the whole thing memorable as they reflect on it.
That covers quite a few different things, but hopefully that answers some of your question. It's not a singular thing that makes a piece good or not. It's a number of different aspects and how well the writer takes advantage of the medium. It's a very different type of story telling and arguably harder to pull off than traditional short stories because of the stricter word count limitation.
