all above is correct, and slice type has to be the highest number of knight types, if you also have the same number of another type, you get a non-typed ship.
So really just make sure you have 16 or more slices type knight's and you have more slice type knight's than any other type of knight.
if people need more help here is a link
http://flowerknight.wikia.com/wiki/Whale_Airship
if you do not click forum links a google search will get you same information.
I found that page explained it really well, though just remember that is all the info is for the DMM site, but otherwise in my experience perfectly accurate.