What cover is attached to the ebook on your Fire?
Recheck the metadata for the book while in calibre and "check metadata" for the covers available. If the cover you want appears and is an "Amazon" provided cover you may want to choose that cover. Transfer it to your Fire and check if it the correct cover.
I wonder if the problem could be the file type of the cover in not compatible/accepted by the Fire.
I've not had any problems getting a cover I want transferred with the book but I've had to look around online for some more obscure books to get the cover I want then convert the file type to an acceptable type.
Hope this helps.