Originally Posted by QuiltE

Welcome to the Quilting Board, JakRabbit!

Absolutely!! ... flannel backs are often used for kids quilts. Adults too!
Best to wash all your fabrics (if you haven't already), as they will shrink at different proportions. For me, I tend to wash flannels more than once, and try to get the shrinkage under control before I start cutting.

I don't know your machine, but I am sure you can quilt with it.
Most any machine you can. Even the old treadles.

Good Luck!