What material is best for a mouse pad that stays flat?

Natural rubber is your best bet for staying flat over time, assuming the pad is at least 3mm thick and properly cured. Cheap rubber pads may curl due to under-vulcanization, but letting them sit under a book for a day usually fixes it. Silicone bases are almost immune to curling but have a grippier feel, while polyurethane foam bases curl most often.