I will let you know how easily this transition goes.
UPDATE: It was easy — as it always is — to find the app in iStore and to "purchase" it. It's free, and it downloaded normally. I opened the app and saw that I needed to enter my email address and Amazon password, and that caused the downloading of "Archived Items," which was a list — with book cover pictures – of the 11 books I'd already bought. When I touched the name of one item — it happened to be "The Best and the Brightest" — a download of the whole text of the book happened in a few seconds. At that point I could display the text on the bright, clear, small iPhone screen and flip the pages easily with my finger. I'm delighted!
[Typo corrected: "finger" not "figure." Yikes. The image!]