Hi, I saw your post and knew the exact flannel to suggest. Clothworks. It is the best but then I saw the under 3 bucks. Sorry I could'nt help. I have never had any luck with any of the Joann's flannel, they pilled badly for me.
I can't find good quality flannel for under $5. It all seems to pill pretty bad. I found some Amy Butler flannel which usually runs $10 a yard at fashionablefabrics.com for about $5 on clearance, it has yet to pill.
I just ordered some flannel from Fabric.com and I am SO thrilled with it. I prewashed it and hardly any pilling, just a tiny bit. It really feels so nice, and it is double napped.
I bought this -- Extra Wide Flannel Fabric. It is HUGE - 108 inches wide. It's $7.50 a yard but at 108" width that works out to about $3.00 if you bought 45" width. In this width they only have white and off white, which is all I wanted anyway.
I have not tried any of their other flannel, but you can order swatches and toss them in the wash to see how you like them. I can't say enough good things about this extra-wide flannel though, it's wonderful.