Can anybody tell me what material with this tone cap

Perhaps a film capacitor?

http://www.electronics-tutorials.ws/capacitor/cap_2.html

http://www.planetz.com/guitar-tone-capacitors-material-types/

 

Looks like a cardboard tube, so it is probably film based.

 

Note the one that looks like it on the right of the row of caps in the last link:

"mystery vintage gray cylinder (now identified- Mullard Mustard polyester film/foil),"

Which seems to confirm it as a polyester film capacitor (which as you can see was dipped in some kind of goo to seal it.) A film cap is the right kind to use for tone circuits. Stable values and low loss.

Generally in my tone circuits I use the Yellow ones a couple to the left which is essentially the same capacitor. I use them just because I have a drawer full of them.