Amazon has a powerful customer base, and they have a great technology in the Kindle FIre. By the power of these two things combined, there is very little chance that their new phone won't catch on. Android proved that Apple could be defeated when it came to phone sales. Amazon can do it with their technology and android OS.
The new phone offers amazing new features especially for people who love Amazon and frequently make purchases there. The have fantastic apps and even a 3D screen. The only downside to the phone is that you have to buy it online and there isn't a way to test it out in stores which may dissuade people from taking that risk.
The smart phone market is already diluted, with many competitors trying and failing to take down the top companies who already dominate. Amazon have a chance though, they are already a household name with their Kindle tablets, so phones which offer similar service are a perfect way to compliment this. If they play their cards right, it is not so far fetched to believe they could find their place at the top with like likes of Samsung.
Yes, the phone will develop a market share because of the integration with Amazon shopping and Amazon Prime viewing service. There are enough consumers that use those products that would benefit from a phone that is fully integrated with those services. However, I do not believe it will be able to compete with the Iphone or Galaxy.