I think this would be very complicated to do via dummy. It is possible to set up a dummy unit to attack in your unit's place so that you can apply stacking poison, however it seems there's a hard coded lower bound to attack speed: 0.1 second.
That means you cannot use a single unit to apply poison on all units hit by Phoenix Fire - the attack speed will cause huge delays.
That may not be issue by itself, but you want a stacking poison on top of that, meaning when the unit with Phoenix Fire damages same unit with the spell, the poison must be reapplied by same dummy unit to ensure correct stacking. Since Phoenix Fire is AoE, this would require you to create and track 1 dummy per unit with Phoenix Fire per unit damaged by the spell.... i.e. very ineffective and you would see it in intensive fights by sudden drops in FPS.
So probably the more reliable way to do this is to just trigger the entire thing. Create and track 1 dummy per unit with Phoenix Fire. Use modified Acid Bomb because it does the same slowing and damage over time like Poison and cannot be dispelled. Make the modified Acid Bomb a unit spell and either give it multiple levels, where each level would represent X stacks... or leave it at one level if you are running WC3 on 1.31+ as then you have the ability to modify spell's fields via triggers.
Anyway, when you detect unit taking damage from unit with Phoenix Fire, use that unit's dummy to cast your modified Acid Bomb on the target.
If you set up dummy unit correctly, it will be able to cast the spell multiple times without delay.
The hard part would be tracking how many stacks would be on given unit and when each stack would end. Whenever stack is applied or expires, you use the latest dummy unit to recast stronger or weaker version of the modified Acid Bomb to imitate stack change.
