When a tile is touched (and not already moving), set an instance variable on this tile, for example "isReadyToMove=true".
Then when the screen Is In Touch and there is a tile which is ready to move, compare Touch.speedAt(0) and Touch.angleAt(0). For example, if Touch.speedAt(0)>100, then start moving the tile in Touch.angleAt(0) direction, rounded to 90 degrees.
When the tile starts moving or has arrived, and when any touch has ended, clear the isReadyToMove flag.