That's wonderful Nicole that your son has gotten infected by the
rocket stove bug!
A lot of the rocket stoves on YouTube are made from cinder blocks or regular cement bricks that will work just fine for a beginner level experiment to see how one works. Its fast, cheap and you can take it all apart when your done if the fad wears out and use them somewhere else. Cement doesn't like high temperatures for long term use though (they will spall - basically break down and crumble apart)
A better brick though would be one made from clay. Home Depot often carries them. Sometimes if your lucky, they can also be found for free in the classifieds. The soft red clay bricks (you can use them like chalk on the sidewalk) would be the ones to look for. These were the original rocket stove bricks used by Ianto Evans that got a lot of the rocket stove information out there.
By the looks of it, the ones Jennifer is using in the photo are special refractory bricks made for
wood stoves and kilns. Some are dense and heavy (perfect for holding heat in a pizza oven) while others are light and insulative to reflect the heat back to make the fire burn even hotter and very clean. These ones are much more expensive unless you can score a deal like Thomas & Paul did (from the same source).
If you really want to delve into the different kinds of bricks, I know Erica Wisner made a post a while back describing all the various bricks out there and a description of each. I'll include a link when I find it for you. Happy building!
EDIT: Here it is. Probably more info about bricks than you never thought possible:
Fake-fire-brick