Fair point Elim, and I've now removed and re-installed the app. Now, the rotation lock is gone, the page rotates with the device, but there's no way to lock it.
What appears to have happened is that the technique Amazon used to pop the little padlock icon onto the display when the device was rotated no longer works, so, although the config setting is present, there's currently no way to change it. When my Flyer was upgraded, I had the rotation locked and the app honoured that under HC, but now, after a re-install, the rotation setting is back as unlocked and again, there's no UI way to change that.
Before the Kindle app got a lock setting, I used Tasker to switch off Auto-rotation when the Kindle app was active. At least now, I have the choice to go back to that. I emailed Amazon support who suggested I call their helpline to go through some live assistance... I'll let you know how I get on..
T-Mobile MDA Vario III
O2 XDA Mini S