If you don’t have twrp recovery in your device you can follow this link to install TWRP recovery in your Fire Tab 7.
Warning: We gammerson.com is not responsible if you damage or brick your device. Do it at your own risk and follow the instructions properly.
#How to Flash Cm12.1 Rom on Fire Tab 7 2015
2.Then place it on your SD card on you tab 7.
3.Now turn off Fire Tab 7 and turn ON by pressing Power button +Volume Down button to boot into recovery mode.
4.Now Press volume down button to highlight Recovery option on Bootloader then press the Power button to Select it.
5.Now your device will boot into TWRP recovery.
6.Swipe below arrow to flash Cm12.1 rom, in your device and then similarly flash 5.1 GAPPS in it.
7.Now go back yo recovery Home then do Clear cache, Clear Dalvik cache.
8. Now reboot your device.First boot will take some time after few min Cm12.1 will be installed in your device.
9.Done!You have successfully flash Cm12.1 Rom.