I use a layer of cotton/flannel and a layer of fleece and have been for years and never had a problem. I throw things away when they get chewed, but even if they do a ton of damage in a single day - i have never had an issue.
That said, when I make things for a friend's chinchilla, I use fleece only (and only seamless designs) because supposedly chinchillas can ingest the fabric if they chew it and exposed seams are an enticement to chew and if they ingest the woven fabric they can become impacted. I am not exactly sure how that works not having had a chinchilla, but it is what I have heard from the chinchilla community, so I follow their instructions. Rats will never ingest the fabric they chew, so impaction is not a risk.
I think the hammocks work out better with a layer of each. My hammocks tend to be pocket style, so they can go into the fleecy warm inner area when cold or lay on top of the cooler cotton surface in warmer temps. Two layers of fleece produce very thick hammocks - especially if making pocket hammocks where several layers are sewn at once, and they can be a challenge for some sewing machines with so much fabric needing to pass under the presser foot, but a layer of fleece and cotton is just about perfect. And the cotton fabrics are always sharper and more vibrant than the fleece patterns.
But that is just my preference.