There actually is a little evidence to suggest he may be the son/spawn of an Old God, but we'll come back to that later. It's far more likely that he's just an especially strong Loa god. Loa spirits have more than one origin, they don't all come from the same background. Some of them are feral spirits, primal powers of nature. These would be your animal gods we've seen so much of in Zul'Aman and Zul'Gurub. A Loa could be the spirit of a dead ancestor (such as Zanza) or even a true God, like Elune. No, they don't worship Elune, but a Loa could be something like Elune.
The Trolls have far, far more gods than anybody else. That we know of, anyway. They all aren't quite as impressive as Elven gods, but a few of them are. To name a few of the Loa gods: Bethekk, Hir'eek, Shirvallah, Ula-tek, Ogoun, Shango, Zanza and of course, Hakkar.
As you probably know, the Trolls were the dominant race on Azeroth for a very, very long time. The Trolls had multiple world-spanning Empires when the Night Elves were just establishing themselves. The Trolls were bashing heads with the Aqir long, long, long before the Night Elves ever considered going to work with the Qiraji (who evolved from the Aqir later on).
Over those years, the Troll Empires declined slightly from the many wars that were fought between the Trolls and the Aqir, the Trolls and the Elves, and the Trolls and the Trolls. The nail in the coffin, more or less, was the Sundering caused by the Night Elves and the Highborne. The Sundering shattered the world, and therefore also shattered the Amani and Gurubashi Empires. They survived, but only barely. Fear of destruction and starvation became their top concerns, rather than their dominance of most of the world.
The various Troll tribes and empires looked to their Loa gods to help them get through these hard times, and desperate times call for desperate measures. The Gurubashi found Hakkar as their answer, or more likely, Hakkar found them. Through him, the Gurubashi managed to pull their Empire together and they began spreading throughout the areas surrounding their capital city once more. All that they had to do in exchange was offer up endless amounts of blood sacrifices to Hakkar. No big deal!
A sect of priests had become especially close to Hakkar: The Ata'lai. When the rest of the Gurubashi Empire began to understand the nature of Hakkar and his intent to enter the physical world, they rose up against the Blood God and the Ata'lai. The power of all of the strongest Gurubashi warriors barely managed to push the Faceless One (yes, another nickname) and his priests into Zul'Gurub, and a small contingent into the Swamp of Sorrows. After a very long, grueling battle, the Gurubashi warriors managed to defeat and banish Hakkar once more. Unfortunately, defeating Hakkar was almost like shooting themselves in the foot. Banishing him was the right thing to do, but losing his influence and losing as many warriors as it took to bring him down ultimately caused the downfall of the Empire. Their Empire could no longer be considered such. They were a tribe, and not much more than that.
The Ata'lai priests that traveled north to the Swamp of Sorrows did not give up their faith in Hakkar, however. They built a temple, a shrine to the Blood God, called the Temple of Atal'Hakkar. It was here that Jammal'an the Prophet, their High Priest, would choose to resummon the Blood God in exchange for immortality. Ysera thought this idea sucked and knocked the Temple to the bottom of a lake.
A band of heroes (us) also infiltrated the Sunken Temple many years later. Luckily, they were able to stop the summoning. Unluckily, they handed the Essence of Hakkar over to some Troll that used it to summon the Faceless One in Zul'Gurub later on, away from the interference of the Green Dragonflight.
It seems that at this point, the remnants of the Gurubashi Empire have gathered in Zul'Gurub, realizing that summoning Hakkar back into their world may truly be their only hope. High Priests of other tribes attempted to stop the Blood God, wielding the power of their personal Loa gods, but Hakkar and the Ata'lai were too much for them. However, rather than kill them outright, Hakkar dominated their minds and enslaved their Loa.
Trolls from the neutral region of Zandalar heard of this, and rushed to Stranglethorn to stop the empowerment of the Blood God. Many heroes were recruited by the Zandalar, and eventually Hakkar was defeated once again. And again, he was banished from the physical world. While we may hope he's gone forever, it is probably only a matter of time before we see him again.
That is, more or less, the full known story of Hakkar the Soulflayer. However, let's go back to that bit about Hakkar being related to an Old God. If you read this past Sunday's Ask a Lore Nerd, there's a question there about Tirisfal, and what it is. The response to that question discusses the possibility of an Old God beneath Tirisfal. There is a little evidence in the form of a research journal you find questing for something called a Bloodstone. There's a pretty good chance that this stone has Old God origins, and it seems to have vampiric qualities. It drinks, absorbs, and thrives off of blood. Hakkar the Blood God behaves much the same way. He is empowered by blood sacrifice, and we witness firsthand that drinking in the blood of his enemies cures even the worst wounds.
It's not very strong evidence, but if there was any evidence at all in-game that he may be an Old God or related to an Old God, it would be that or the fact that Eranikus fell to the Nightmare while in close proximity to Hakkar, and the Emerald Dream's corruption is (probably) caused by the Old Gods.
For more information on the subjects discussed here today, I recommend taking a look around Wowwiki. A lot of the quests associated with this stuff takes place in content nobody does very often with the launch of The Burning Crusade. Zul'Gurub, the Ahn'Qiraj Scepter events, et cetera. Wowwiki will be your best best.
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