Violent Flourish acts as a normal hit with your weapon, just with the chance of an added effect of stun; i.e. if it lands, you will do damage like a normal hit, and gain the TP to go with it.
This move can skillup weapons. This can be useful when skilling up longer delay weapons. It will reset the swing timer but can proc skillups.
If the Stun effect is successful, it will state this in the chat log along with the damage. If unsuccessful, it will simply show the damage.
Note that this ability has two accuracy checks: a physical check (to see if Violent Flourish actually hits) and a magical check (to see if the stun effect is successful). This is similar to the Blue Mage spell, Head Butt.
Rate of stun success is fairly high on weaker monsters.
Rate of stun drastically increases from successive applications of Stutter Step, as the stun effect of the flourish is a magical effect.
Stacks with Sneak Attack, allowing a bypass of the physical accuracy check if successful. This may also increase chance of stun.
Wearing Etoile Casaque greatly increases the chance of stun.