My rayon is from a big box of CelluCotton Beaty Coil I bought from Sally Beauty a few years ago, that will last me about three lifetimes
(part number 44060).
I don't know how thick your flat roll is, but maybe how I do mine might still help you. Mine comes off in a rope that's way too think to use as is. I cut a few inches in length and split off a thickness I think is about right. I compress one end and give it a try, then either add a bit from the discarded part or pull a little off what I'm using until it feels good. The squeaking noise you mention is a really good way to tell when it's right, though IMO it is also part feel as well. Using this technique you can try a bit more rayon and a bit less until you think it's right, then vape and re-wick as desired.
One other thought. I generally use either 27 or 28 gauge wire. With cotton, when I feel I have enough of it in the coil I place the tip of a finger lightly on the coil to stop it from moving too far due to friction from inserting the cotton. With rayon, I
need to do that or my coil will be ruined. If you use thicker wire this will be less useful but might still help a bit. I can't imagine wicking 30 gauge or thinner wire with rayon unless I wrapped the wire around the rayon before mounting it, it's just too flexible.
Experimenting with this is easy, cheap and not really too time consuming. And once you get a system going that works for you you'll have it licked. Best of luck with it
ETA: Sorry, I read your text as flat roll, not fat roll, lol.
Then again, I now realize we're using the same rayon so just ignore the 'brainfart' part of my response