Listing a free book on Amazon
It took me a while to figure out how to list a free book on Amazon. For other platforms such as Smashwords there is an option to mark it as a free book. This then filters through to their affiliated retailers such as iBooks, Barnes & Noble and others. Unfortunately, there is no option when pricing your book on Amazon to mark it as free.
To get your book listed as a free book on Amazon you first need to have it listed free elsewhere. Then, sign in to your Amazon account, find your book and scroll down to the Product Details section and to the "Would you like to give feedback on images or tell us about a lower price?" you need to paste the link of your free listing from a different platform here to prove that you have your book listed elsewhere as a free book. once you have done this Amazon will ( at their own discretion ) price match the book. This may take a few days.
What you can do to speed up the process ( their decision making ) is to then email them to inform them of what you have done and why.
A point to note: make sure you update your keywords ( i.e "free ebook" "free horror story" etc BEFORE you contact Amazon to request that they make your book free. The reason for this is that you cannot set your book to be free, and this will not show on your product listing page. What shows is the price it was before Amazon made it a free book. When you change the keywords to reflect this it will the follow through the process of pricing and will NOT allow you to list it free and will not allow you to save fully until you have selected a price. That means you will need to price it and then contact Amazon again to request that they again price your book as free.
So, ensure you change the keywords first for the book you want as a free book and then inform Amazon as above that you wish them to mark your book as free.
update to the above.
It seems that you are not permitted to change the keywords to "free book" and then contact Amazon to get them to price match your book so that it is listed as a free book. Do this, and you'll get a stern email from Amazon about deception etc...as the book at that time is not free...even though that email will be the reply to your email asking them to make if free based on the links you have provided to show that it is free on other platforms!
So, it looks as though you do need to tell them first to make it free, wait for it to be listed as free, then update the keywords to reflect this. However, I can see no way to update only the keywords without being prompted to update the pricing also, which will not allow you the author to mark it as free. So, once you have completed your listing for key-word update you need to contact Amazon a second time to make if a free book...again.
There is a new service that Amazon offer whereby you can create a paperback version of your ebook for customers to purchase. Then you can select an option for customers to be able to download a free version of your ebook...if they purchase the paperback version of it.