I actually have a test project similar to this. It uses the linkedTools behavior. It was difficult for me to understand at first but simple now. You create a link object over the current tiles and link them. The tiles need to be on a grid but otherwise it will link them no matter which side the next tile is on. You then link a start and end object to the group. The behavior then moves an object from tile to tile.
project: (click the green [code button] and download zip
Try it: Every time you click the button, it moves the target sprite to the next square.
EDIT: I needed to update the project. I had removed what I thought was an unneeded pick all players it was needed. So, I put it back in.