Wondering why you want to try felt? It's so much more expensive than flanel or as Amma mentioned - batting.
I use flanel, have no problems with stuff sticking to it. One exception was the landscape quilt I was working on. After a while, after layer and layer of fabric and polyester thread to hold each little bit of fabric on, the quilt was far too heavy and I had to hang it with binder clips. Other than that ... I've got a finished bargello (my avatar actually) that is about 30" square just "stuck" to the wall and it stays there - no pins. Hasn't moved in months.