I used cotton for his gray wrap. I also used cotton for the black and white undercoats.
The first time I made his top coat with the xtra long sleeves I used black suiting fabric. It was a little too floppy for my tastes but I know a few Undertaker cosplayers who used this fabric and liked it.
When I remade the coat I used twill, which I liked much better.
When you say knee highs, are you referring to the boots? In the anime his boots are low enough where you can see the striped socks that he wears. But maybe his boots are higher in the manga...(?)