I use some dial calipers to measure patch material.
If you aren't familiar with them take a look at this link
http://compare.ebay.com/like/180931667818?var=lv<yp=AllFixedPriceItemTypes&var=sbar
These measure thicknesses or outside dimensions, inside dimensions and depths to an accuracy of .001 (one thousandths of an inch).
Normally the outside or thickness measurement is done right at the tips which have a very narrow width to them but this almost knife like feature can easily crush cloth giving a lot of variation in the reading.
I've found that using the flat area back towards the body is less likely to crush the material.
In any case, the user must feel the drag or resistance of the caliper jaws on whatever it is measuring to get a good reading.
There will be some drag but not a lot. It's difficult to explain in words.
There are electronic versions of the calipers at most auto supply stores and although they are accurate and inexpensive (if you call $20 inexpensive) my biggest complaint with them is the damn battery usually goes dead just when I want to use them.
As to how thick a patch should be? IMO that depends on the type of gun, the depth of the rifling grooves, the size of the ball and the phase of the moon.
Well, maybe the phase of the moon isn't that important but the patch has to do several important jobs.
It must seal the bore and this includes the rifling grooves. This is especially important with heavy powder loads in a rifle. Less important in a pistol.
When wrapped around the ball its thickness must be equal to the the rifling groove diameter or preferably, a little larger.
It must be somewhat compressible because the lands between the rifling, being smaller, will need to compress the material or it will be impossible to load.
It must transmit the rotation of the rifling to the ball as it is fired.
This usually isn't a problem if the depth of the rifling creates a need for a fairly thick patch but in barrels with very shallow rifling it could be a problem. (I don't want to get into a "skipping the rifling" debate but IMO rifling depths shallower than .003 often shoot very poorly unless the patch is a very tight fit.)
This transmitting power thing in my opinion also requires a tight weave to the material.
I've seen loose weave patches end up as flying threads as they settle to the ground after they were shot.
It must be able to withstand the heat of the burning powder. Some synthetic materials (and silk) tend to vaporize from the blast.