Seaside, I will have to dig up the old data, but the answer is no. Flash is unaffected by Fight or Flight just as it is unaffected by the damage reduction from Shield Oath. Flash is not damage-based.

You might also consider Second Wind on WAR. This is affected by Berserk because the ability increases attack power and not damage. It is not, however, affected by Maim, which increases damage, or Defiance, which decreases damage.