Is There A Concern For A Type Of Cloth We Can Set Coins Onto?

Doesn't make sense to me.

Raw coins should be stored in mylar generally.
Don't store in cloth.

I we're talking about using a cloth lining on a coin tray, you need to make sure that the cloth doesn't contain anything sulfur-containing or acidic that will leach out over time and damage the coins. Unfortunately, there's no real way to test for this unless you actually put some coins down on top of them for years. But as a general rule:

"Natural" fabrics such as cotton, wool* and silk are less likely to cause problems than synthetics. Both will degrade over time, but the synthetics are more likely to contain acidic plasticizers and such. Use un-coloured/undyed fabric rather than dyed fabrics, as it is the dyes, rather than the fabric itself, that usually causes problems.

* - Wool can be high in sulfur, depending on type and origin. Raw wool is more likely to cause problems.

If we're talking about short-term use, such as a temporary display, or a cloth to put down on a hard surface when handling coins, then it is less critical and pretty much any cloth ought to do.

Soft cotton is best as a temporary backing, but rolling up coins in cloth for storage is not a good idea.

I have a friend that stores his six figure coins (large cents) in cotton liners. He has done this for decades and never had any issues.