I think the real determination of this is what is available as organic cotton. Are your embroidery threads and interfacing etc. also organic??
There are (online) shops that do specialize in organic fabric. My usual go-to for online shopping is equilter, they have a number of options. Doing a quick search I found several flannels at Joann, they were even reasonably priced but a lot of them were actually not available, still there were some that would suit your request. Remember that pretty much all flannels shrink so go large on your order
