I know what effective health means, I just thought you were including the regen and passive from the Shield as Shield only gives 80 health and you somehow came up with 150-300. Even so, my point still stands. Lets use Pantheon for example with 15 bonus AD and his Q against Flask and Shield
His Q deals 86
He is able to spam Q 6 times before running out of mana at ~24 seconds
You typical top laner has around 32 armor from runes so that equals to 65 damage from Q
65 x 6 = 387 damage
387 damage in 24 seconds. Lets say your champion starts out at 600 hp initially without items.
600 - 387 = 213 remaining HP
W/Doran's Shield HP will be 680
Since Spear is targeted, it will block 8 damage so thats 58 damage
58 x 6 = 348 damage
680 - 348 = 332 remaining health
Shield's health regen is 1.2 per second.
1.2 x 24 = 28 hp regenerated over 24 seconds
332 + 28 = 360 remaining health
So you would only be taking 320 damage with 360 HP (52%) left with Doran's Shield
Now lets look at Flask
600 - 387 = 213 remaining health
2 flasks = 240 health regenerated over 24 seconds
213 + 240 = 453 remaining health
So you would only be taking 147 damage with 453 HP (75%) left with Flask.
In order for Doran's regen to be of equal value to the champion HP with the Flask in this calculation, you would have to wait for over a minute. Now you still have 1 flask left over and 3 health pots. With Doran's Shield you have 1 health pot. Now note that its single targetd. If I were to use like Pantheons E then the gap would further widen.
Doran's Shield will only outvalue flask if you're against the likes of Fiora but thats only if you are going all in balls deep with no disengage.