Here's a picture of a wild monkey in Thailand flossing. There are a lot of modern pictures and video of primates flossing and there are a lot of ancient human skulls with grooves between their teeth that suggest people have been flossing for a long time (more on that in a future post).
Dental historians, such as Drs Matthew Sanoudos and Arden Christen of Indiana University, have detailed the writings of Levi Spear Parmly, who suggested the use of waxed silk to clean between teeth in the early 1800s (1). Parmly's writings seem to be the oldest printed references to dental floss.
You can read the 3 lectures Parmly gave in New York City in 1820 with this online link (and save the $1.50 (now $20) it would have cost you for admission).
Parmly didn't go into the details of flossing in the lectures. Here's the key page that describes floss from the end of the third lecture.
1. Sanoudos M, Christen AG. Levi Spear Parmly: the apostle of dental hygiene. J Hist Dent. 1999 Mar;47(1):3-6.