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I'm not sure all ebooks have samples.
That said, make sure you are looking in the Kindle Book Store, so you don't see books that don't have an ebook version; then this is what you are looking for.
View attachment 19985
Strange. Did you try searching for and looking at the same book I'm showing, just to be sure?
Also, make sure you've registered the Kindle app on the iPad. It may not show the option if it does not know there is an ebook reader to send it to.
Hmm, is it a reasonably current version of IE? I think they are up to 9 now, aren't they.