I can't deny the story flowed interestingly, and it took a lot of risks that may or may not pay off. This is certainly a fic where one's mileage may vary, because the vagueness in the writing style certainly turned a lot of people on, but, personally, I was kind of left asking "Huh...?" until the last sentence of every vignette.
Make no mistake: your writing style is beautiful, poetic. The prose is very delicate, employing distinctly different styles to help you go into the mindset of the central character of that segment. However, here's where we move onto the essential flaw of this fic: you don't know WHO the central character is.
I'm sure you intentionally wrote it to be disorienting, but, personally, I felt disoriented to the point where it affected the quality of the fan-fic. It truthfully left me unaware of where we were, who we were rooting for, etc. It was stream of consciousness to the enth degree, abandoning, for the most part, the physical world in favor of thought process.
For the most part.
Additionally, I really don't know what the three vignettes had to do with one another. They seemed sparadic, almost a little random to be honest. At times, I figured they'd all tie together in some way, but they never did. That could've elevated your to a higher level. Unless the escapee girl controlled a Houndoom that attacked the kids in segment two, in which case the fic failed to really bring that to my attention. It leaves the fic open to interpretation, yes, but also leaves this one prone to simply Wild Mass Guessing, too.
Don't get me wrong: this fan-fic was still awfully enjoyable, but more in the sense that the style was distinct and intriguing than the actual plot and story were engaging. Indeed, while you characterized the Houndoom awfully well, the jail segment seemed almost a bit random. The most powerful point, however, was the children segment, in my opinion. Following the Houndoom scene, you knew Houndoom needed to kill kids, so when the child goes missing, well, your mind goes to dark, horrible places, which I commend you as a writer for. The fan-fic is worth it for that nightmarishly depressing image which a lesser writer (probably me) might have gone into a large amount of detail into. It's what you DON'T see sometimes that's worse than what you do.
All in all, nice effort, I enjoyed it, but I can't say I loved it, either.