As @deng mentioned above, the Amazon tablets have historically had locked bootloaders -- they won't load custom ROMs. The XDA guys seem to believe it's unlikely you'll ever be able to load Cyanogen on one of them.
> The XDA guys seem to believe it's unlikely you'll ever be able to load Cyanogen on one of them.
The first-generation Fire tablets definitely support Cyanogenmod, though it was a bit awkward to get around the bootloader lock at first. Are the newer ones not supported?
almost no Android phone allows custom os! understands this.
all Samsung phones can only be flashed because someone leaked a internal tool. and still, there must be a huge community effort to get the kernel and drives for each model.
now keep in mind that this huge community effort doesn't exist even for for-developers v phones, such was the case with the moto x dev edition. with phones like fire, it's practically non existent!
Android devices are not open by any means. they just have a lovely stubborn community.