Jack's a professional writer, but not all of his stories make it into print. The stories on his blog are the flash fictions or shorts that he "word doodles" when he feels like being creative but not doing any actual work. They get his thoughts out in a more creative form than just posting about his dreams, but he doesn't think they're worthy of paid publishing, so he archives them on his blog for the public to enjoy (or be disturbed by).
While these stories are fiction, they are always based on dreams that Jack has had, so they should all be set in some sort of actual reality. Jack can, of course, bend the rules as he sees fit, but a big portion of the story should be realistic in nature.
You may choose to just make up a story from scratch (a lot of these are caught-in-the-moment sort of life stories), or you may use one of the dreams that Jack posted on his blog as inspiration. If you do use an existing dream, please note that at either the beginning or end of your submission.
It is not necessary to make up a dream before you make up a fiction story.
Please use the stories on Jack's blog as a style guide so you can mimic his voice while writing: http://jacksdreamlog.wordpress.com/