Diaper flannel will work fine as a cleaning patch, but it doesn't have a strong weave to prevent gas blow by when used as a shooting patch. It will work after a fashion, but accuracy on target will suffer.
The fabric store won't know the thickness of the materials. You need to take your vernier calipers or a micrometer to the fabric store and measure the thickness in the store. Bear in mind that the fabric in the store has sizing which will affect the thickness measurement. Washing is required to remove the sizing. Drying in a hot dryer will tighten the weave of cotton drill, pillow ticking, mattress ticking, denim and canvas to make the fabric more robust when used as a shooting patch. Canvas will have a weight associated with it indicating the approximate thickness. Cotton drill cloth (my favorite is the #40 utility cloth at JoAnn's Fabrics) will eventually be 0.017 or 0.018" in thickness. Pillow ticking will be anywhere from 0.013 to 0.015. Mattress ticking will be from about 0.018 to 0.020. Denim will be all over the thickness scale and may not always be 100% cotton. Canvas will range from 0.020 to 0.024. Always check to be sure that you are buying 100% cotton fabric. If you are buying linen, be sure that it is 100% flax linen or a linen cotton blend. Modern linen doesn't always have the tight weave that was used.