Yes, you can reuse them. Couple of things to keep in mind.
1. Make sure ALL old addresses have been removed or thoroughly marked out. If you don't remove all old addresses, you run the risk of the package getting delivered to the wrong address. Trust me - it has happened!!
2. Make sure the box is still in good enough condition to be used again. I have seen some flat rate boxes that were pretty beat up, especially if they have had traps shipped in them.