Can straps and chains be routed outside the rub rails on a flatbed trailer?

Yes, at least in the Unites States. U.S. rules don’t prohibit the practice of routing tiedowns around the rub rail, or attaching tiedowns to the rub rail. Both practices are prohibited in Canada, however.

Keep in mind that it’s a good idea to avoid routing tiedowns outside the rub rail whenever possible, since the rub rail is designed to protect the trailer and tiedowns from damage.