i dont know how to best use powdered abrasive on fabric.. it seems to hold some, but shed it over time, i think mixing it with some soap might manage to hold it better, but still wash out alright if you change your mind.. maybe someone else can provide some insight on, for example, chromium oxide powder v.s. chromium oxide paste.

anyways, this isnt about linens performance, but if you are looking for more fabric medium to work with abrasives go to the auto wreckers and get some cheap seatbelt fabrics..
if you get the kind where the fabric is sewn right onto the metal tounge of the buckle you can easily tie a loop of strong string/cord through the hole in tounge in such a way that it hangs flat without twisting to one side or the other.. not what you were asking about, but something else to consider.

i imagine linen webbing and cotton webbing will perform similarly when it comes to the use of CBN powder.. seatbelt may be a little different.