The Kindle Fire HD 7" has one of the best screens for enjoying multimedia content and reading. The stock OS did not have much value compared to third party ROMs. I have been using third party ROM and has settled with official CM11 for quite some time (about a year) until last week. xda Forum contributor faZevoLv has released an unofficial OmniROM running on Lollipop 5.1 - which installed smoothly with the latest GApps found. (I tried CM12 beta, too. I installed but it gave a series of FC upon booting up. I believe it might have to do with the version of GApps but did not research further on the correct version). The user interface is very responsive, animation is quick and I have experienced no lag. Make sure you have a second bootloader before installing OmniROM. http://forum.xda-developers.com/kindle-fire-hd/7-development/rom-omnirom-android-5-1-t3052050
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