I don't think AoEs count as DoTs. Don't quote me though, I could be wrong. *I* would assume they don't, though, but I've never really thought about it.
As other people have pointed out, the additional damage over time Flamestrike does is akin to ground AoE DoT effects like Consecration and Death and Decay.
Flashburn affects DoTs done by your fire spells on specific targets.
What it does do though is that when you crit with flamestrike, it puts up ignite that benfits from flashburn, woooo... I guess it's pretty obvious but there you go.