Tested! Turning off Javascript works!
All you do is pick your book then checkout like normal.
After checkout when you get to the Get For Kindle page disable JavaScript
Menu\Browser Settings\Disable JavaScript
Then
reload the page or you'll get an error.
Now
Click Get For Kindle and it will take you to Amazon's page
From there you can get your book sent to your K3.
Remember to re enable Javascript after you are done.
It's alot of typing and navigating but it works.

I would not want to do this on the K4's keyboard.