I bought the Kindle Fire HD 7 inch and the HDMI cable works perfectly with my High Definition Television. Its great my gaming, surfing the web and even streaming movies from the Amazon library as well as Youtube.
Yes, the Micro HDMI (Type D) to HDMI (Type A) cable works on all Kindle Fire HD's 7" & 8.9". This is the cable you will need to connect to your big flat screen TV. Keep in mind, the non-HD Kindle Fire's only have one USB port for charging the battery and transfer data (such as photos, music, etc.) and WILL NOT work with any HDMI cable.
I had a Kindle fire 7 and it was not HD. as I remember it only had usb port... The 8 inch Hd has both a Hdmi and a usb... Now if your 7 has a HDMI port you willl not have any problem hooking it ti your Hd TV. Flay