Theoreticly, it's strong on champion that are going to be harassing from a distance, over time.
In practice, because of it's build path, it's best on champions like Amumu, Singed, and the like. Because it stacks with their damage over time, because the health scales better on them because they'll be building tanky items which synergize with it. It's really a AP-Tank-item, not a Burst AP item.
Additionally, look at it this way: A burst mage takes you to half health in their first volley, then the blackfire proc ticks away for 3 seconds, taking 5% of your current health, equal to roughly 2.5% of your total health. Compare it to Singed, who runs in, poisons you, the proc immediately starts ticking away dealing 2.5% of your current health, which is almost full, and this the damage it deals is actually about the same: 2.5% of your total health for 3 seconds. The difference is that because it's a DoT effect instead of a burst effect, it is reapplied with each poison tick, and lasts an additional 3 seconds after the last tick, and thus the total time it's effect is active is going to be more like 6-10 seconds, depending upon how long you stand in the poison.