What fabric should I use for a cuddle cup and cozy?

Flannel or cotton will work for the outside part. Are you using it on fleece bedding or shavings? If other parts of your cage is shavings, smooth cotton fabric might work better than flannel.

You can use Fleece on the outside of the cuddle cup as well, Flannel could work, hopefully someone who has made cuddle cups will chime in.

I suggest you to use fleece on the outside of the cuddle cup because if you put the cuddle cup in the cage and your puppy pees it, the fleece will absorb better the pee and the cuddle cup will stay dry longer than using cotton or flannel

I make lots of cuddle cups and sacks.

A 100% cotton/flannel on the outside, quilters batting in the middle and fleece on the inside.

Flannel is best in cages that do not use lose bedding, while smooth cotton is better for cages with lose bedding. Either are perfect for cages with fleece.

When I make testing bedding I use broadcloth, its super cheap but make sure its 100% cotton. Oh and it only (or so I've only found it) in solid colors but its easy to find matching fleece for it.

If you need any help message me I'd be happy to help in any way I can.