There are several other major considerations too that need to be taken into account when determining if just the King bricks will be strong enough. Start with the load the roof will put on the walls needs to be taken into account. The load from the roof will be a combination of the weight of the roof itself plus the snow loads etc. that will be on top of the roof. Actually, when loads will also affect the strength of the structure.
I highly doubt that a wall built with just a single layer of King Bricks will have sufficient strength for what you're looking for. You may be able to build a double wall of King bricks that are locked together to get sufficient strength or you could build an interior wall of concrete blocks or even a framed interior wall to give you the extra strength required.