Flame Spiral's effect line says
Until the start of your next turn, any enemy that enters a square adjacent to you or starts its turn there takes 1d6 fire damage. An enemy can take this damage only once per turn.
while Lightning/Frost Weapon has as its at-will power
All damage dealt by this weapon is (cold/lightning) damage. Another free action returns the damage to normal.
So would Flame Spiral's effect damage count as "damage dealt by this weapon", if cast though a Lightning/Frost Dagger or Staff?