I don't think it has anything to do with the restrictiveness, just that it was not very compelling and had 2 weird gimmicks no one really had a use for. That combined with the low visibility of Amazon as a phone manufacturer, I can really understand people held off buying.
Microsoft is having enough problems convincing people that a 3rd place app store is worth developing for, how was Amazon supposed to get in?
I like how Blackberry is considered 'effectively dead'; I've felt the same way since they failed to react to the iPhone.
The iPhone has a VERY LARGE ecosystem of software and hardware to support it. There is a lot of value there.
But the Fire Phone didn't have that. It ran a version of Android so they could have had a lot of stuff but instead they chose to prevent that. In the end it cost as much as their competitors but had no software and it's only unique features were somewhat gimmicky.