Replicating that painting would be difficult, I think, because cloth doesn't wear and tear like that.
The cape in the painting has a number of almost perfectly circular holes of various diameters, some superimposed on top of each other.
Most fabric is woven on a loom, the warp and weft threads running straight and at 90 degrees to each other. Thus cloth has a "grain" one could say going horizontally and vertically, and that's how cloth wears and tears.
So there's a choice to be made, whether to distress fabric in the way it distresses, or recreating that illustration.
About replicating that painting, I suppose if you had the right fabric you could burn those circles, or cut them out. Unless you bound the edges of each cutout circle the fabric would begin fraying along the horizontal/vertical axis of the woven fabric.
Felt isn't woven, it's pressed, so felt would avoid those problems. It's easy to cut holes in felt, and once cut felt doesn't fray much.
About distressing cloth, I came across a great YouTube video about recreating the look of surviving clothing from the Middle Ages. I don't remember what the video was called.
When I've distressed cloth I've used sandpaper and thinned-down Liquitex acrylic paint. It's not as realistic as Fuller's Earth but it stays put forever.
