The skill is tagged with spell doesn’t that mean it scales with flat spell damage?
However when testing between 2 indentical unique weapons, one normal, the other 1LP enchanted with +47 spell damage and there is absolutely no increase at all.
The exact same highs and lows within the 20% variance rate.
I assume you recast it when switching weapons? It does have the spell tag, but it doesn’t do damage directly to mobs so there’s nothing that would use any flat spell damage. If you’re talking about the Doom Brand node, that applies an ailment (Doom Brand) that triggers Soul Blast that has the spell tag so it should inherit any flat spell damage from gear/etc (but not from the Dread Shade skill tree).
I’m talking purely about dread shade’s damage I have no dots or any special effects taken in the talent tree.
I cast dreadshade on my single skeletal mage (I’m completely naked) and let him shoot the dummy until dread shade completely runs out.
Then I equip a 2handed staff with 90 flat spell damage and 380% increase to spell dmg. (a massive increase)
Still gives me the exact same numbers, dread shade does not scale with flat spell damage or % spell dmg despite having ‘‘spell’’ on the scaling tags.
I just don’t get it. 
Because it’s a flat Buff, that you apply with a (Necrotic) Spell.
It doesn’t actually do Spell Damage itself, similar to Sigils of Hope for Sentinel/Paladin.