Di, it's not widely available at the moment and I'd never taken much notice of it before but it said on the page that the Kindle was eligible for it. From what I could see delivery is free on orders over £40 and £3.99 if below that, but there's a £15 minimum spend. It's for Prime customers.
When I was placing the order it gave me a choice of 2 hour time slots throughout this afternoon.
https://primenow.amazon.co.ukSaundra, I've never tried one of the Kindle tablets, this is just the Paperwhite. I like those because they have the built in back light so I can read in the dark.