Although I think the Harbor Freight micrometer is a bit more than $10 and the $20 digital caliper is acceptable enough for our purposes, the torque limiting screw will not compress the material as much as it will get compressed during loading. When I use a micrometer for measuring patch thickness, I use the method proposed by @Ontario47. At the fabric store, the material has sizing which will result in a reading that is off and way off for measuring the compressed thickness. Bulk material needs to be washed and dried to remove the sizing. The material takes up the lubrication better and will tighten up the weave and survive the loading stress.I judge the thickness of patch material (pre-lubed) with a micrometer that has a torque limiting thumb screw/clutch so that the crushing force is uniform. A $10.00 digital caliper from Harbor Freight is good enough with a little practice. Buy some patches that say what they think the thickness is and see how close your test tool comes. Again the truth is at the range, and with your expectations. Hunting deer cleanly is far different than winning a bullseye match at a known distance.
By the way, make sure the crown at the muzzle is smooth. Use your thumb and wet or dry sandpaper to smooth out the crown. This will ease loading and possibly prevent the sharp lands at the muzzle from cutting the patch.