Not sure about the specifics of the woodland scenics mat, but I've used various railroad ones in various projects over the years.
A spray adhesive tends to work best if it's paper backed.
Also, if the board is going to be a flat one, get a dowel longer than the board is wide (A cheap one from the hobby store works well, or even a pipe piece you might have). Open your mat up and roll it, flock side in, on the dowel before putting it in place. When you're ready to mount it, the dowel allows you to have a nicer, even pressure on the mat as you lay it out and is less likely to have bubbles and other issues when it goes down.