Hmm, well Rubber Cement would remain flexible but long term flexibiity Im not sure of. Next that comes to mind is the Kel Seal elastomeric coating I use from a paint store, smooth grade would glue it down and remain flexible, but never have used it to adhere paper. The paper strikes me as the unknown to roll up as a matt though. There are plastic window shade material that is highly flexible, lies resonably flat that might sub in for the backing mat,

, if mounted on a bar you might be able to use the pull out - roll up effect of a window shade..
These are all just fast thoughts on your post.