I've thought about washing rayon wicks, but it's easier to install a new one. Every Rayon wick I remove just has a gray tint where it was under the coil. The rest is clean (I vape mostly unflavored juice or light shades of flavor). Very few of my juices are crud makers. I could wash and dry and recycle, but it's not really worth it. By the time I do that I can cut and install a new one.
I usually run a Rayon wick until it's time to dry burn and clean or replace the coil.
This chart is pretty interesting. It details the qualities and burn points of fibers. Cotton and Rayon are on there as well as most of the fibers we use in vaping.
Fabric Mart :: Burn Test Chart
I guess we've detoured this thread into a Rayon discussion. I'll back off and let people talk about cotton.