Yes, Cocofloss can be recycled! We consulted with Jessica Coe (an avid Cocoflosser and recycling consultant at Cascadia). Here's the run down:
Our current packaging (the box) is made of 100% recycled paper fibers. Toss it into the paper bin along with your newspapers, magazines, etc.
The plastic floss container is made of polypropylene and can be recycled. It'd be ideal to remove the metal cutting blade, although you do not need to remove it. Most plastic remanufacturing plants can take care of the blade for you.
Unfortunately, Cocofloss's polyester threads cannot be recycled via recycling carts due to the complexity of the recycling process and the fact that Cocofloss is waxed.