If you have your music in iTunes on your computer pc or mac, you may want to sync or transfer all your audio songs & playlists to your Kindle Fire HD. You can sync music using android app on your Kindle Fire. If you want to use Amazon Cloud Player, you can use Amazon Music Importer to copy mp3 songs or iTunes to Kindle Fire HD instead.
If you have media PC or Mac for managing your iTunes music or playlists, It is a good idea to sync your music to other devices like Kindle Fire HD to enjoy music on the go. If you download any music from Amazon MP3, you can sync it back to your computer too.
How to sync iTunes Playlists to Kindle Fire HD/2 via WiFi/USB
1. Download & Install iSyncr Desktop application on your Computer PC or Mac. Make sure this application is running on in windows system tray. Also, You need to have iTunes installed obviously.
2. Download & Install iSyncr for PC (USB & WiFi) (iSyncr for Mac (USB & WiFi)
) on your Kindle Fire HD or Kindle Fire 2. It costs about $4.

3. Open iSyncr app on your Kindle Fire & Go to Tools > Settings and configure sync settings.
4. Go to WiFi tab > It searches for available iTunes libraries. If you don’t see your computer name, select manual option and enter your computer IP address. It displays your playlists after connecting to iTunes. Select what you want o sync & Tap Sync. You can also connect your Kindle Fire to your computer using USB cable & sync it.
It syncs both your music & videos on selected schedule to your android tablet. If you have large collection of music to be synced for the first time, you can connect your Kindle Fire to PC or Mac via USB to transfer the songs quickly. iSyncr also transfer your listening songs back to iTunes. This is useful for generating smart playlists.
You can try iSyncr Lite for PC for free. This Lite version has a limit with number of songs you can sync.
Also, read how to remote control iTunes without transferring iTunes music to Kindle Fire HD
isyncr was recomended for use on Click BBC television but it seems it is not available for use on my Kindle Fire. I hope it will be available to UK Kindles soon.