I have mounted a few of these. They are usually paper that has been glued to linen or some other flexible cloth. These were field maps from the mid to late 1800's, and because they were durable, they are sometimes the only copies that survive. I treated them as I would a poster mounted on linen. We have a number of them in our local courthouse.
Usually, with a few stitches at the top and a decently spaced mat, they hold up well as long as the customer hangs them and leaves them alone. Theyhave usually been stored rolled, so there aren't too many creases. I have held them under weight for 6 weeks or so, and then they were reasonably flat. They are usually heavy enough that gravity actually makes them look better over time.
Occasionally, there is a fussbudget that wants something perfectly flat for decorative purposes. (I may be cynical, but suspect taxpayers are still ultimately footing the bill). I scan and print them and return the original to the archive and everybody is happy. And since I have the digital file, it easy to produce duplicates of popular maps.