Most Kindle ebooks have DRM (encryption) which ties each file to a single device or app (e.g. a particular instance of K4MAC).
Calibre can manage ebook files with DRM, but, as you have found, copies of your DRMed K4MAC ebook won't work on your Fire.
If you want to use Calibre as a central repository for your ebooks, then use the 3rd party plugins for Calibre than strip DRM. These work on import to Calibre, so you would have to re-import your K4MAC ebooks for this to work. See Apprentice Alf's Blog for more on DRM issues.
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