Dental Lace (direct to site/referral with coupon) sells biodegradable dental floss, both silk and vegan, which comes in small glass containers. They also sell bamboo-handled toothbrushes and toothpaste in tablet form.

You can buy directly from their website, or you may find their floss in other stores that specialize in "green" products. I strongly suspect that Public Goods' store-branded floss is from the same manufacturer as Dental Lace's, with the major difference being how you want your glass container to be decorated. After that initial purchase, you can purchase the refills from either place and they'll work fine, though Dental Lace's packaging is more environmentally-friendly.

What I like about the silk floss: it's sturdy. The first time I ever tried biodegradable dental floss, it was some random brand that came in a cardboard box I found at Whole Foods, and that stuff basically shredded as soon as it came into contact with enamel. Dental Lace's silk floss actually holds up to use. Unfortunately, the same can't be said for the vegan floss; it has a much higher tendency to shred than the silk kind. The little glass containers really are adorable, like little spice jars.