Two main reasons:
1. I'm not convinced you read or fully understood the Permission article before posting. Many of the questions you asked in this thread are answered there, and you didn't seem to know the requirements for a permission request—for instance, it took my prompting to even bring the issue of the writing sample into the conversation. Whether you haven't read it or just didn't get it, either way is not a good sign. Reading and the comprehension of it are both important to PPCing.
2. Your writing needs more work. The basic SPaG mechanics are mostly there, but overall, it seems like you wrote this piece in a hurry and haven't really looked it over since, or consulted a beta about it, either. There are some systemic problems, and more questions raised than answered for the reader. I'll bring some of them up as I go through the main issues.
First, there's a whole lot of telling instead of showing. The whole history section in particular is made of this, and then the characters tell us what we've already been told with their dialogue about having a job to do. Readers want to learn about the world by experiencing it through the characters, not have it spelled out to them ahead of time only to have it repeated. You could have set up the setting by showing us how Kaite and Daisy became Dream Knights, for instance; by describing the world as they move through it. Think of the narrative as the lens of a camera, only it lets in sounds and smells and textures and emotions as well as light as it passes over the story. Usually the camera is whatever character we're following at the time, so we experience things as the character does, but as you get more comfortable you can play with different perspectives and such.
Furthermore, regarding that particular bit of dialogue, the characters should already know this stuff, so it feels forced and unnatural on top of being redundant with the narrative. People rarely feel the need to tell each other things they already know. Also, if Daisy is really so young and air-headed as to forget what she's supposed to be doing at any given time, how is she suitable for what seems like important work as a Dream Knight?
Second, there are some serious contradictions. For instance, we're told it takes more than twenty minutes to get to the Nightmare World because you have to cross a long, thin cloud bridge on the way. However, when Kaite uses the star button, the other Dream Knights are there instantaneously, "on cue." How did they get there so quickly? Where did they come from? Were they in the Nightmare World all along? If so, what are Kaite and Daisy even needed for? Shouldn't this huge army have things under control?
Then there are sentences like this one: "There were no guards, due to the fact that everyone felt like guards were necessary."
Did you mean "unnecessary"? Even if that's the case, how are guards unnecessary if Dream Knights regularly turn up to keep the Nightmare World in order whether they want it or not? Don't the Nightmare World citizens want to keep them out—I mean, isn't that what a gate is for? I definitely didn't get the impression that the Knights were invited over.
Third, some things are just downright confusing, like this passage: "Most of the citizens retreated back into their houses, even if they were on fire. The citizens who had burning houses then stepped outside their homes to complain about it."
Did they... somehow... not know their houses were on fire before they went in? Otherwise, why would they go to all the trouble of going inside first if they were just going to come back out and complain? It doesn't make sense. Are they supposed to be dumb? Silly? What?
Also, this passage: "Both girls faced away from the gate to see various creatures attacking each other, various people setting houses on fire somehow, and weapons flying, both figuratively and literally."
This is very nondescript and paints a terribly vague mental picture. What are these various creatures? Since they are "various," what different kinds are there? Who are these various people? What do they look like? Are they different from Dream World citizens? What kind of weapons do they have? Are they throwing swords and guns at each other?
Also, beware the narrative "somehow." It's a red flag to the reader that the writer either has not stopped to think about what is happening or couldn't be bothered to clue us in, either of which is bad news. If the writer doesn't care to put the effort in, why should we? In this case, you could have just left the word out and it wouldn't have been an issue; we'd just assume the normal methods of setting fire to buildings, like torches, or maybe fire spells, since magic seems to be a thing here.
Altogether, that's why I'm saying no for now. I'm sorry if it seems harsh, and please understand I don't mean all the questions to grill you. They're just things that came up as I was reading. I ask them to point out areas where you could improve the story, if you want to rewrite it for next time. 'Cause there can always be a next time. {= )
~Neshomeh