As the name states, this weapon was intended to be connected to the Four Kings in the New Londo Ruins, either as a dropped weapon, or as a boss soul weapon. However, as it was cut from the final release of the game, it is unknown how the player would have obtained it.
Due to its nature as cut content, the Four Kings Sword is simply a texture in the game files. This means that even if the player modified their save file, it would not have its own stats anyway, as an existing weapon's model has to be overridden in order to 'obtain' it. Hence, the weapon can only be seen by those who are modifying the game to use its model.