Moved the folder for .azw3 to /mnt/sdcard/Kindle, and it no longer gives me an error message when I touch Read, but it also doesn't launch the reading app.
If I have a .mobi, it doesn't matter where it is, though it makes more sense to use /mnt/sdcard/Books than the /Kindle folder.
For the moment, I think I'll just tell CC to only do .mobi. I'm assuming that Calibre will honour that and do an autoconvert?