I can't speak for felt, but I have done flannel and cotton batting.
I had some flannel yardage that I tacked to the wall one night just to try it out... worked well, but it was just a very temporary measure because my flannel was printed and pretty tacky looking up on the wall.
I went to Joann and got several yards of batting off a roll. My plan was to wrap it around foam insulation boards and mount those to the wall. I just used big flat thumbtacks (had them for mounting embroidery to stretch bars) and tacked it up to my wall floor to ceiling. I had meant for that to only be up a week or two until I could get around to fetching some insulation boards... but well, that was months ago.
The batting works great, probably a little better than the flannel did.
Tips/Notes:
1 - you want your design wall material to be taught against whatever you mount it to. Your fabric will stick to it better if it isn't hanging loose. You can google or search pinterest... there are lots of options for mounting temporary walls or making free standing walls
2 - I have white batting and it isn't a problem, but Kaffe Fasset makes a gridded gray flannel specifically for this purpose and claims that you shouldn't use white because the bright white can be "distracting"