Oh yes, the clay is just an addition to the regular cement/sand mortar. The easiest way to go for a small job is to buy the premixed sacks of mortar that are sold in the
concrete block aisle of you
local home improvement store and then add maybe half as much sifted clay. When you add
water to this mix, you are not looking for the thick milkshake like consistency of block mortar, but add more water until it is thin and soupy. When you butter your bricks, it
should only be about 1/8" thick (or less) and you won't be able to get much mortar out of the joint if you tap on the brick. It also helps to work with wet bricks when you are laying them, as you want the mortar to flow easily over the surface of the brick.
In this video, you can see that he is slapping on the mortar very thin, like a plaster.
http://www.youtube.com/watch?v=zW9NLc26F3g
If that plaster sets up between two bricks, it holds them together, but there isn't much surface area of the joint exposed to the heat. And if a little clay on the surface of the joint gets vitrified from the heat, no problem.