willuwontu: Desna's states you make a SINGLE attack and multiple damage rolls... You can keep going round and round but it's STILL A SINGLE ATTACK... If the damage rolls were actual strikes then they could crit, have sneak attack added [and add flaming] each 'effective strike'.
Unless and until you can PROVE that "make a single attack" and "If the attack hits" somehow means multiple attacks, then I have nothing else to say to you: I disagree and think you are 100% wrong as flaming only adds damage once per attack.
PS: site acting funny, ate 1/2 of post... :(
EDIT: I think you rely on strike meaning hit/attack but look at Magic Missile once: "A missile of magical energy darts forth from your fingertip and strikes its target, dealing 1d4+1 points of force damage." A strike without a hit/attack. So we're in a squares are rectangles but not all rectangles are squares scenario. Even if you can prove 100% that attacks are strikes, that in no way proves strikes must be attacks or hits. You can't sneak attack with a magic missile, but with strike = hit it would be possible.