Question about few skills

[Alumno Superstes]

Warrior: Grey Warden, shield user

I use Fury of the forge strike skill, adds burning (=affliction)
THEN there is passive called Fighting Dirty which adds affliction based damage type done.

I had idea, if you mix those, would I add extra burning dot with it? since This strike ability already adds it.

I have tried to chek it my self but really can not see..