Yes there is. You have to go to the menu and go to the HDMI settings. There is a pass through option. I am not sitting in front of my equipment right now so I am going by memory but you will see it. Let me know if you need anymore help.
The "ipod" input is just usb. It can play music from any old usb drive. I imagine if you can plug the kindle into a pc and play the music from the pc you'd be able to play music from your kindle thru the reciever. Of course if the kindle has a port for headphones, it will most defintely work. In either case you likely won't be able to control the kindle thru the reciever remote. Hope this helps.