Hi Judy! Sorry to hear about your friend. :crying:
The fall 2004 issue of Knitty was dedicated to breast cancer. A woman that had cancer said that chemo caps made with cotton, microfiber, silk, and cashmere are good choices because they're soft and don't tend to irritate super sensitive scalps. I have heard that synthetic fibers are generally tolerated better than animal fibers, but everybody is different.
Another site recommends softer yarns (such as cotton), Lion Brand Microspun (nice because it's 100% acrylic and machine wash and dry, but I think is a bit difficult to work with), "fun fur" yarns because they're soft and lightweight, hats made with thinner yarn (particularly good for summer weather, especially cotton). They also say that thinner, seamless, non-lumpy caps are good for sleeping and increased comfort. They have some nice patterns on the site too, although the "Inside Out Chemo Cap" pattern--which appears that it was originally a pattern for a hat knit in the round which was adapted to be knit flat--is very wrong. I tried knitting this myself, and the pattern was fine until I got to the decrease part. I tried to adapt this to work out and even contacted the owner of the website for help and asked for help on this forum, but it still wasn't right. I'm not sure how the lady who submitted the pattern got hers to look as nice as it did following the pattern.
Lion Brand's site has a few patterns for chemo caps using their fur yarns; one is coupled with Microspun, and another one is their Incredible ribbon yarn (this one is crocheted though, but I'm sure if you wanted to make a knitted hat out of the ribbon yarn it would be just as fine).
There have been some very good previous posts about chemo caps which included links to patterns and such:
Post asking for yarn choices
Another post about yarn choices and includes links to some patterns
chemo hat patterns
post about fiber content of chemo caps
I hope some of this helps. Lots of love and hugs to your friend, and how kind of you to knit her a hat!