Originally Posted by
SaberMaxwell
RDM autos themselves are based on their Strength stat (there is also an auto-attack statistic on the weapon itself), and Brotherhood should (I'd have to go and check) affect Fleche for instance. However, given Fleche is not a weaponskill it would not grant the Monk any chakras. For comparison, in a party with a second Red Mage, their embolden would affect your Fleche but your embolden would not affect your own because of that distinction.
It's good that RDM autos don't hit very hard, or Red Mage would be at a severe disadvantage if it ever had to go to range for ranged DPS mechanics.