My first attempt at this problem was to use Scanner Pro to scan my Kindle. Scanner Pro worked as designed, creating an OCR’ed PDF. But, that was not useful for Drafts, because I needed plain text, not an OCR’ed PDF.
So, I opened the file on my iMac with PDFPenPro and used it to convert the PDF to plain text. It did it, but with so many formatting errors that it would have been easier for me to type the page than to try to fix the document it created.
Based on the recommendation from @derekvan I tried the app TextGrabber. It works amazingly well. It does the OCR trick, but does not create a PDF. The scanned text is immediately available to send to Drafts (and other places) using a Share menu.
I ran two experiments. The first was with my Kindle. I scanned a page of text. The text was delivered to Drafts with no errors. The entire process takes only a couple of seconds.
The second experiment was with a book I was holding in my lap with one hand while using my other hand to take the picture with my iPhone. It was definitely not a precision operation. But, the text from the page I scanned was sent to Drafts with only a single error. One Drop Cap on the page was misinterpreted.