The main reason for lining the inci after turning has ended and before the hatch is to help the chicks find their feet and stop them slipping around on a smooth surface with not much friction. In the early hours when newly hatched, their leg muscles are still weak and their legs can splay out sideways if they slip, and this can cause a condition called spraddled leg. The malformation can 'set' very quickly, in the hours they're drying off in the incubator, so the chick can't walk properly as it develops. Efforts to correct it by tying the legs together with splints are sometimes successful, but it's very tricky and obviously you want to avoid this, hence cotton or similar fabric can be used as a lining on the floor of the incubator to provide friction. Any sort of comfortable cotton fabric will do so long as it provides grip and reduces skidding, but is smooth enough not to tangle fibres in the chicks's claws. It does also help keep the incubator clean inside and should be thrown away afterwards to avoid infection, before you sterilise the incubator. (BTW, clean the incubator ASAP after the chicks are transferred to the brooder, as it gets harder once the mess has stuck on.)
See this thread posting.php?mode=quote&f=7&p=37481
Good luck with the hatch, let us know how it goes!