36 years ago - Jack Chavez is born in Gotham.
30 years ago - 6-year-old Jack's father dies. He starts training his dogs to fight.
25 years ago - 11-year-old Jack falls in with Mama Fortuna's street thieves, and becomes a star pupil in a small underground dojo.
20 years ago - 16-year-old Jack beats Selina Kyle near dead for disrupting Mama Fortuna's street thieves. She follows him to his underground dojo, where she trains alongside him. He nearly kills her a second time before he is cast out.
13 years ago - 23-year-old Jack commits his first murder while robbing a house.
7 years ago - 29-year-old Jack fashions himself into Hellhound to become a costumed hitman. He attacks Catwoman, who brings him down & hands him over to Batman.
2 years ago - 34-year-old Jack manages to maneuver his way onto the Suicide Squad. He is killed by Atomic Skull on his first mission.
Hellhound is sometimes used as a deliberately unmemorable villain: when you want a reference to a bad guy that no one cares about, Hellhound is a decent choice. He's a pretty cool LOOKING character, with his stylized ninja togs and knife collection, and he's notably deplorable what with his penchant for using fighting dogs. Still, he seems to stand out more for being a sort of background, generic masked bad guy.
So why are we using him? Very specifically, he's a great fit for our failed Suicide Squad team. we wanted to have a few members of the team that Atomic Skull kills when he goes berserk, and while Magenta is notably tragic, you can kill Hellhound without too much trouble. His ties to Catwoman are pretty interesting, but once that single story plays out there's not much else you have to do with him.
Occasionally, characters are built for a singular purpose, and Jack Chavez is a great example of it. Still, he's a cool LOOKING bad guy, and it's fun to fold him into our timeline.