fine linen as in table cloths, is usually rather thin. And unless it has been washed or is very very old, it has sizing which keeps the linen somewhat thinner than after the sizing is washed out.
That brings us to some folks theory of patching. Slow motion video has shown us that there is some extent of blow by of smoke and gasses regardless of how tight the combination. You can load an extra tight combination that requires a mallet and tungsten short starter to swage the patched ball into the bore. But the seal, doesn't get that tough again when being forced back out by ignition. The patched ball does swell some due to obturation, (the hammering effect from behind caused by ignition) but so do most patched ball combinations. now we know that a combination that is too loose, affects accuracy and fouling, but where between 5 pounds of pressure to load the patched ball and 150 pounds of pressure is the seal as good as it gets? The rifling configuration can effect this, so some guns with square deep grooves may require much more pressure to swage the patched ball into sealing the corners of the grooves. On the other hand shallow round bottom rifling may take much less pressure to seal the bore. The thickness and tightness of the weave affect the ability to swage that patched ball. In some guns, a thin loosely woven patch and larger ball can more than adequately seal the bore. A heavy nap on flannel can seal the bore as well as .022 ticking. The idea is to seal the bore with as little deformation of the ball as possible. A mallet and starter undoubtedly deforms the ball. My target barrel has oval bottom grooves that are deeper along the lands than in the middle of the groove. The grooves are 5 or 6 times wider than the lands. As a result, I could shoot very well with a .005 muslin patch and .445 swaged ball. Easy to load, sealed the bore adequately and very very accurate. So the thickness of a material does matter, but only to the extent that the bore is sealed.