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.
Cocofloss fibers are made of polyester, and they can be recycled along with other plastic materials.