Just to be sure (apologies for asking the obvious) - is it actually a Kindle book (.mobi format) that you are trying to open? An app will not appear in the "Open In" option if it cannot read that particular format. Or, now that the iPad could have more than one page in the "Open In" pop-up - did you see if the Kindle app is on another page in that pop-up?
If the answer is yes to both - then maybe a restart or a reset of the iPad is in order (fixes most of the iPad "glitches"). To do:
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears.
If that doesn't help, try this last step...
Reset: Hold both the power and home buttons until the screen goes dark and the Apple logo then appears (the slide to unlock screen may or may not appear). Once the logo appears, release the buttons. After a time, your homescreen will appear. Please note that it may take some time for the Apple logo to appear or for your homescreen to appear (or both). This is normal. Eventually, the homescreen will appear.
Hopefully, some of that will help. If not, holler back and we'll take another shot at it.
Marilyn
