My opponent attached Reinforced Armor to a Jasmine. I played Flaming Arrow on it. She took only 1 damage from arrow's instant 2 damage. I compared texts of each card. It seemed to me Flaming Arrow's effect overrides Reinforced Armor. However, GuestofHonor said the mentioned armor ability should be something like Legion United's ability as Reinforced Armor is not an armor but a human ability - attachment. You can compare the two cards texts too.
At this point, I searched for Banebow's ability+Reinforced Armor as I remembered there was a bug reported about this. I saw BB's ability damage is reduced by Reinforced Armor and it is recorded as a bug. To my surprise BB's ability and Flaming Arrow has the same text. Thus, I think this should be a bug. Reinforced Armor shouldn't reduce Flaming Arrow's damage too.
Bookmarks