I've already bought what I thought was a cable that would allow me to connect my sister's Kindle Fire HD 6 t her telly, but the connector to the Kindle turned out to be too big, and only for tablets (this is a reader I guess). Before I waste more money can anyone point me to a link where I can buy the proper cable?

Thanks
TH

Try one of these.

http://www.amazon.co.uk/Amazon-HDMI-.../dp/B00KVSAJHK

You'll need an HDMI to HDMI cable to go with it.