It does not stack with itself, but it will reapply each second an enemy stands in the poison. Also, the effect is only half because it's a DoT. That causes *~0.833¯% of their current health in magic damage* for each second an enemy stands in the poison, and then two more seconds after they leave. Compare that to the damage he is already doing, and it's not that much. Examples:

*****If you want to skip over the math, look for the item names in bold towards the bottom*****

At rank 5, Poison Trail does 70 base damage. Assuming a 2000 HP opponent:

70 / 2000 = 0.350 = 3.5% of *max health*.

Blackfire Torch would add, assuming opponent is at max health:

2000 • 0.00833¯ = 16.6666¯ damage

16.6666¯ / 70 = 0.238 = 23.8% of Poison Trails base damage.

At 75% max health:

1500 • 0.00833¯ = 12.4999¯ damage

12.4999¯ / 70 = 0.179 = 17.9% of Poison Trails base damage.

At 50% max health:

1000 * 0.00833¯ = 8.3333¯ damage

8.3333¯ / 70 = 0.119 = 11.9% of Poison Trails base damage.

At 25% max health:

500 • 0.00833¯ = 4.1666¯

4.1666¯ / 70 = 0.060 = 6.0% of Poison Trails base damage.

Compare that to the flat bonus Blackfire Torch's bonus AP (50) would provide:

50 • 0.30 = 15

15 / 70 = 0.214 = 21.4% of Poison Trails base damage

The bonus AP does the same amount of damage as the passive at ~1798 HP.

So, total at 100% max health, assuming 2000 HP:

23.8% + 21.4% = 45.2% of Poison Trails base damage.

At 75%:

17.9% + 21.4% = 39.3% of Poison Trails base damage.

At 50%:

11.9% + 21.4% = 33.3% of Poison Trails base damage.

At 25%:

6.0% + 21.4% = 27.4% of Poison Trails base damage.

You would, however, get two extra ticks of the Blackfire Torch effect at the end, skewing this slightly.

Now, compare that to, say, Rylai's, a common core item for Singed:

80 AP • 0.30 AP ratio = 24 damage

24 / 70 = 0.343 = 34.3% of Poison Trails base damage.

How about Wooglet's Witchcap?

100 AP + (100 • 0.25 bonus AP) = 125 AP

125 AP • 0.30 AP ratio = 37.5 damage

37.5 / 70 = 0.536 = 53.6% of Poison Trails base damage.

Now, to compare the items as a whole (bonus HP from mana on items factored in):

**Blackfire Torch** - 2890 gold - 21.4-45.2% (assuming 2000 HP opponent) of Poison Trails base damage, 387.5 HP, 350 Mana

**Rylai's Crystal Scepter** - 3105 gold - 34.4% of Poison Trails base damage, 500 HP, 15% slow on Poison Trail.

**Wooglet's Witchcap** - 2700 gold - 53.6% of Poison Trails base damage, +10% MS, +25% AP

Rylai's provides more utility and 112.5 more HP for only 215 more gold (the mana on any item, after bonus HP is calculated, is almost useless on Singed), while Wooglet's provides you with more damage, plus it gives you more AP out of your other items and a movespeed buff, all for 190 *less* gold.

TL;DR:

With these numbers, Blackfire Torch is a subpar item compared to other common options, such as Rylai's and Wooglet's. I'll do 3000 max HP next.