Natural silk dental floss either sold in a reusable/ recyclable glass bottle and metal lid combination, or as a refill on its own.
 
This floss is 30 metres in length and coated in minty candella wax which is plant based with no plastic in sight. 
 
Why silk?  It's not really because it's luxurious.  In fact, silk is strong, effective and compostable so an ideal plastic-free swap.