Old pillow cases are often linen. Hold them up to the light, and if you can't see through them it's good. A pillow case lasts a Long time.
At a farm sale one time, I bought a mattress ticking and still have miles of that , and it is Good. ( Blue & white striped)
For hunting I use a bullet board with a few in, but have a strip of patching soaked in deer tallow, hooked to the shooting bag. It is cut through into square patches with only a corner holding, and a patch can be torn off for use very easily. Square patches never hurt accuracy as far as I can tell, and it saves a lot of messing about.
Cheers,
Richard.