Iceblossom

It sounds like you and your neighbor will be setting up a new program.

Different groups/different hospitals will have different needs and very often some very different requirements. For NICU, all cotton (batting and fabric and some say thread too) is common. Flannel is usually ok, but prewash the heck out of it to shrink first! I haven't heard any complaints about using Warm and Natural. In my previous sewing group one of the ladies was a big provider of infant quilts, while I made a couple of tops for her, she did all the quilting down and such.

You don't want too many seams or lumpy spots. Not the time to make narrow log cabins and such.

I just joined my current guild they support many groups, for NICU it just says:
NICU noted that they have new beds and have asked for quilts of larger sizes – 36×36 or 40×40. Fabric and batting must be 100% cotton. It is also okay to back a quilt with flannel, but two sided flannel is too heavy.

Which is actually good for me, I find it pretty much impossible to design anything smaller than 36x36, but I can follow patterns that small.

Edited to add a set of twin tops I made from jelly rolls for Janice the quilt lady to finish. That was a flannel back.