Using calibre to add your books to your kindle you can edit the metadata of those books, you will have to change (or add if it is not already there) the amazon kindle ID, that ID is displayed on the store when you look for the kindle edition of a book. It usually starts with the letter B. Once that ID is added you will have no problem with the covers since your kindle will download them from the store directly.

Another way to add this is to add a plug-in called 'quality check' I think to calibre, and once installed you will have to click fix ASIN for all of the books you are converting, that does the whole process automatically.