How to put vinyl click-together flooring up against cove base tile?
The only proper way to install a floating plank floor is UNDER the wall trim ( or cove base tiles in your case ) so that the expansion gap stays hidden under the trim as it fluctuates with expansion and contraction. 

You can :

Remove the tiles and install the floor so it goes nearly up to the wall ( leaving an expansion gap ) that the tiles are mounted on. Since there are tiles above the ones you removed you will need to cut the cove tiles to fit back in place. The danger with this is it may not be possible to get every tile off with out breaking one or more. 

OR :

Use a diamond masonry grinder wheel to carefully cut the bottom of the tiles off, install the floor so it goes under them and then use some quarter round or other molding at the transition of the tile and the floor.  

Do they still manufacturer the tile ?, if so i would probably remove the cove tiles and then buy the non cove tiles and cut them to fit after the floor is installed and use some molding at the transition.