Is it okay to write a prologue for a short story?
It's your call. I wouldn't recommend it.
A prologue is generally thought of as a chapter that takes place before the main action. Since a short story should, generally speaking, be around 1000-5000 words, which also happens to be a pretty decent guide for chapter length, in my opinion, if you add a prologue to a short story, you've basically just written the world's shortest novella.
That's not to say you can't include the information other ways. Off the top of my head, I recommend you either a.) add a paragraph or two of information beforehand (Actually, I don't recommend this. It looks kind of sloppy and takes the reader out of the story before you've even gotten them there. It is, however, better than writing a two chapter short story.), or b.) do well placed flashbacks or references; for example: "The dance of the lantern's flame reminded Dana of the fire that destroyed her estate and scarred her face."