Best to ask this question in the
calibre forum.
The iDevice driver for calibre only sees the books installed in the iBooks application.
It is possible, though not trivial to convert the Kindle books to ePub. You first need to retrieve them using an intermediate app like PhoneDisk from Macroplant, then you may also need to remove DRM before converting them, perhaps with Apprentice Alf's assistance.
G