I joined to share this. Hope it helps.

My husband has a third generation Kindle Fire and we wanted to use it to cast YouTube videos to our smart tv. I found a simple way to do this which does not involve any machinations with as many as four separate apps. This is what I did:

1. Turned on the tv (ours happens to be a Samsung, but this should work for all smart TV's).
2. Went to the TV's YouTube app.
3. Selected settings.
4. Signed into his gmail account.
5. Then clicked on "Link TV and Phone" (in reality any mobile device). This produces a code. Write it down. It must be entered exactly.
6. On his Kindle Fire, I went to this address on the web: YouTube.com/activate. Enter it in the address box. Ignore any helpful suggestions. Then hit enter or search.
7. Up pops a screen that prompts you to enter the code. Ours was 4 capital letters followed by a hyphen (yes you must put it in), followed by 4 capital letters. I typed it in. It was accepted and Google prompted me to update security info. You can skip this by scrolling down and selecting later.
8. Now, very, very important. Using Silk, go to YouTube.com. You will see the familiar cast icon. (DO NOT USE A YOUTUBE APP. This does work with them. You will know, as you will not see the cast icon.)
9. Find a video you want to watch. Then hit the cast icon. Your choices will be to view this video on: This device, YouTube TV, Cast..., Cancel. You want YouTube TV. (Cast... did nothing for us.)
10. Voila! You are casting to your smart TV.