Here's Canned Heat playing their song "Going up the Country" at Woodstock:
Here they are playing the song in the official "Woodstock" movie, the version you all saw:
Notice anything different? Answer: the first one has no flute.
See anything odd about this one?:
Answer: the guy "playing" the flute starts out blowing through the wrong end of the flute, but the notes seem to be coming out anyway. How the heck can that happen? Lip-syncing, I guess.
Canned Heat rewrote the lyrics of a 1920's song "Bull Doze Blues", renamed it, and used studio musician Jim Horn to play the flute part. The song went to #11 on the Billboard Charts and #1 in 25 countries, but they only had a flute player as a band member between 2000-2005 according to Wikipedia. The "Woodstock" movie used the studio recording, not the recording played at Woodstock.
There is at least one Youtube version with Canned Heat and a flute player from 2014:
In 1928, Henry Thomas played "Bull Doze Blues" solo with a guitar and a quills (a kind if pan flute) in a neck holder. Here's the original: