I have to agree with the comments saying the UI looks to be a mess. But let's go feature by feature here.
Dynamic Perspective
Some compare this to the iOS7 parallax effect. It isn't quite the same; this is much more movement than the parallax effect, and it appears to be more like a rendered scene (ex, surfaces which extend from near to far, not all flat surfaces facing the user). Personally, I like the subtle depth of the parallax effect. Maybe after the gimmick wears off and Amazon brings out their Fire OS 5 or so, their "perspective" effects will also be subtle rather than jarring.
From a tech perspective, this is very different from iOS parallax, in that it is looking at the user's face (not sure what happens in a crowded room) through a combination of four cameras tracking an emitted IR light field (Kinect-like so far as I can tell). It somehow decides who is the "viewer" in the room and if that viewer's head moves up, down, left, or right, adjusts the view accordingly.
For a single viewer, and if the system works perfectly, it will be better than Apple's accelerometer/level-based parallax movement. But I'm not sure it's worth four cameras and four IR-pattern emitters to accomplish.
Firefly Technology
This is a "great" technology for Amazon. So great, I'd be surprised if they keep it exclusive to their own hardware. I expect to see an Amazon app for iOS and even Windows Phone coming out soon.
That said, the basics are already out there. You have several apps to listen to audio and identify the song/movie/ad, and countless barcode-scanner apps. I haven't seen anything recognizing books and magazines from the covers, but that isn't a huge leap from what is out there (needs access to good book-front/magazine-front images ... which we actually know Amazon does not really have given the number of titles with crappy or even nonexistent photos, but if single-sourced they probably have the closest library out there). Pulling email and URL and phone numbers from OCR'd text is not a great leap forward technologically, but surprisingly I haven't seen it around out there before this (I'd be really surprised if there were any kind of patent on this, though, so expect clones to implement this tomorrow).
What is not out there is a single place to go for all that. That's where Amazon could put out an app to drive people to their storefront to buy a million little things each, or they can seek that Amazon ad as a "feature" on their phone and sell a thousand phones. I'm guessing they will quickly transition this from an exclusive feature to a "hardware works best with" feature (although, honestly, I don't see a hardware-software tie-in here beyond the commodity features all smartphones share).
Mayday
Meh. Might be a great feature for some, but I just can't speak to it because I can't see myself ever using it. Now, providing those help tools to someone besides the dolt in Amazon's call center warehouse? That would be useful, and for more than just "I can't figure out how to turn on the camera!" cries for help.
One-handed scrolling
My phone has that. It's called "hold with your hand and flick up with your thumb".
I see auto-scrolling as useful as the old Microsoft IntelliMouse "trick" of clicking the center mouse wheel on an IE window and dragging to auto-scroll. Constantly scrolling text is very hard to read. Text which scrolls based on a reorientation of the device (again, I'm assuming perfect tracking of the user's face here, but if that isn't absolutely perfect this will be even more of a nightmare) is annoying; I don't hold my phone rigidly pointing at my face when I am reading. I often tilt it, especially when I am looking away at something else in the room. If I did that and looked back to see I'd scrolled ten pages on, I think I'd throw the phone out the window.
In short: clearly demo ware, to be the first "feature" disabled on any real non-teenager's phone.
Tilt navigation
Same as above. Why? This is a hidden interaction, which is easily accidentally triggered, which will not have an obvious "how to get back" when it happens nor "why did that happen", so it will tend to happen over and over again. This is an absolute nightmare of a UI.
FWIW, the "shake to undo" feature in iOS apps is similar, but not quite as easy to trigger. I've been handed phones with a plaintive "why does this dialog keep coming up?" from several people. When I explain it, they get it, but not to the point that they would ever actually use is. An "undo" button on the UI is infinitely more usable, less surprising, and makes people less worried about "breaking" their device by shaking it too hard. A tile doesn't have the "am I going to break it" aspect, but is equally unexpected, inexplicable, and better-off-left-to-an-onscreen-gesture.
Advanced Camera
Well, remains to be seen. Just going off their promotional materials, their nighttime comparison of Galaxy S5, Amazon Fire, and iPhone 5S isn't terribly convincing. The Galaxy S5 has more noise, and the noise is "reduced" using blurring; Amazon says this is "blurry", and it is correct. The iPhone has less noise to start with, and doesn't attempt to reduce it significantly, resulting in noticeable noise. Amazon says this is "noisy" and is somewhat correct. The Amazon phone looks to have started with more noise than the iPhone photo (which is alarming considering it says it used OIS to quadruple the exposure time!), then blurred it away, but not as much as the Samsung phone. Amazon apparently thinks this is "just right". Not sure why that particular setting of noise reduction is a banner feature, given you can adjust the noise reduction settings on most phones anyway. The iPhone is known for its stellar low-noise sensor - not anywhere near on par with a Sony APC-sized sensor like what you'd get on Nikon SLRs or full-frame sensors, obviously, but for the size the iPhone is very low-noise natively. Out of the gate, without years of research, we are to believe that Amazon has surpassed the iPhone in image quality? I doubt it.
OIS
Yes, optical image stabilization is great. On a great camera, it is really awesome. Given the one sample image Amazon put out, though, I'm really worried that aside from OIS, this is a bit of a crap camera.
The downside with OIS is that it reduces "noise" by increasing the exposure times, which lets in more light, so the pixels in the sensors aren't stuck detecting a small number of photons. This means that for a completely static shot, OIS is a great thing. But a typical indoors shot OIS will often be useless.
If you have a great low-noise sensor, putting OIS on it is awesome, because I can then choose. If you are giving me a crap sensor and trying to sell it with OIS, though, that's no deal at all.
Lenticular Photos?
Not sure what to make of this. The display is not lenticular, so far as they are saying (it does "3d" by face tracking, not eye-to-eye stereo graphics). Why would you want to take lenticular photos? Is this some underground "thing" I have just completely missed?
Hardware camera button
I like this. Do worry about accidental triggers, but I like not having to interact with the screen to start taking photos.
Burst capture
Okay, but no frames per second? The name "burst capture" has been used for rates from one-frame-per-second (really) to 3fps (low-end consumer SLR, point-and-shoot standard) to 6.5fps (high-end consumer SLR) to 10fps (iPhone 5S). It has also been misused to describe frames from 30fps video (as opposed to full-camera-resolution frames).
Amazon, what do you mean by this? I'm assuming if it was anywhere near the iPhone's burst mode they would have said so either with a spec or a "better than iPhone 5S" note. But, they don't. I'm guessing they mean ~3fps until they prove otherwise.
Cloud Storage
Unlimited photo storage. That is nice. Only 5GB storage for everything else, though. Not very useful. Can it backup and restore locally, or only to the cloud? If cloud backup is the only option, and 5GB is the only storage for free, either most folks will need to pay for extra storage in the cloud, or they will be going without up-to-date backups. Doesn't sound good.
Overall Assessment
I think Amazon has tried to put too many gee-whiz "looks cool the first time" features into this phone, sacrificing long-term usability. That goes for the hardware and the OS. The OS can probably eventually be fixed.
