Amazon’s Kindle Fire HD is good tablet if you are into Amazon ecosystem. With parental controls and Amazon Prime, you can argue it is one of the best tablets under $200 bucks. Amazon does not have any inbuilt airplay similar to Apple. But you can use android app to stream media from Kindle Fire HD/2 to your big screen TV. This is similar to AirPlay.
Most people have game consoles like Xbox 360, Sony Play Station, Internet connected TV like Samsung, LG, Sony Bravia, or media players like Apple TV, Blu-ray players etc. If you have any one of these and Kindle Fire, you are ready to stream anything to your TV.
How to stream media to TV from Kindle Fire HD/2 via AirPlay
1. Download & Install android app iMediaShare Lite from Amazon AppStore on to your Kindle Fire. It’s free.
2. Launch the app. You can select Photos, Music, Videos, Picasa Web Photos, YouTube or any of the on demand channels. Tap on “My Videos” to see available videos on your Kindle Fire. Tap on “All Videos” to see all the the videos on the device.

3. Select a video to stream to TV. It displays available devices where you can stream to. If you have Apple TV or Internet Connected WiFi or DLNA TV or Game Consoles etc, you should see the list here.

Select the destination you want to use to start streaming your media to TV. You can stream music to audio players like Onkyo, Sonos, Yamaha players etc.
Just make sure your Kindle Fire Hd & device you are streaming are on the same WiFi network. iMediaShare Lite may not display all available devices. It may not auto discover all the devices. You will need to go into that device settings and check if you can access iMediaShare Lite from it. On your device, go to Video Library > iMediaShare > Videos > Now Playing to access Kindle Fire.
For Toshiba TV, enable media render mode by going to TV Setup > Preferences > Network Device Setup > Media renderer setup > Media Renderer on your TV. This should display Toshiba TV in iMedia Share list of avaiable devices to stream to.
Also, iMediaShare has UPnP capability. You can stream media to computer with Windows Media Player acting as UPnP device.
iMediaShare Lite should work for Kindle Fire 1st generation device. You can upgrade to full version of iMediaShare to stream online mpeg videos, online hd vidoe channels etc.
Also, read 6 android apps for airplay