The simultaneous facial and sphincter clench just before a fart is released. 'Flench' is therefore a fusing of the key words 'fart' and 'clench'.
Mary: "My goodness can you smell that? Who farted?"
Joe: "It was Mark, I saw him flench right before the smell hit"
The Knee Deep in Pain book defines Flenches as a combination clench and flex.
Flenches are done to build muscle strength slowly, with deliberation. Flenches help in combating arthritis.