Hi, I finally joined up here, after long-time lurking, to answer this.
I used to live in Japan, and love Japanese cloth.
What you are seeing is almost certainly hemp cloth, probably woven by hand. Japan was too cold to grow cotton, and they didn't have sheep, so no wool. So earlier on (like up to 100 years ago, and up to as late as the 1950s in some remoter areas) you ended up with silk if you were rich, and hemp if you were poor, with a few oddities like cloth made from birch bark in the far North.
If that jacket in the video was made from a second hand kimono, then it would definitely also be lined with cloth that is equally thick, so the stiffness is coming not just from the cloth itself, but from having two layers of cloth, stitched together.
Reasonable substitutes would be linen (choose one which is not too fine), or ramie if you can get it.
They do also sell second hand kimonos online directly from Japan, though I can't give you the name of any sites. I've always stayed away from them for fear of succumbing to temptation!