Why does he does he do this?
There are a number of African cultures spread across the continent that have traditionally used scarification and cicatrisation as a form of body art and Black Panther’s costume designer Ruth E. Carter has championed bringing as much real world African influence into the movie as possible.
In the film he scars himself as you say "for every kill he makes".
According to Gizmodo
In a way, Killmonger’s motivations to team up with Ulysses Klaue (Andy Serkis) to disrupt and overthrow the Wakandan monarchy come from a somewhat similar place. Speaking to EW, Chadwick Boseman described Killmonger as the “voice of a different side of Wakanda” who puts the Black Panther in a difficult political situation. Killmonger’s willingness to hurt and potentially innocent people isn’t necessarily rooted in a desire to be destructive, but to be the agent of change he thinks Wakanda needs.
It’s possible then, then Killmonger might see the kills he’s named himself after not as random acts of violence, but rather, purposeful and necessary things he’s done and would choose to wear symbols of proudly on his skin.
Does it mean anything?
According to Gizmodo
Killmonger’s scars could also be a subtle nod to another comic book villain—Victor Zsasz, a member of Batman’s rogues gallery. Like Killmonger, Zsasz’s body is covered in dozens of carefully carved cuts that tally the number of people that he’s murdered. To Zsasz, his murders aren’t borne out of pure desire to kill people, but rather out of a warped sense of duty to “liberate” people from their lives.
It also tells us as the viewers what a ruthless killer, Killmonger has become and how revenge for his dad and avenging his ancestors has caused the death of several thousands more. It shows us his eagerness to take back the Throne and it shows how much thirst he had for revenge (as he was willing to kill all these people just to take back the Throne)
How does he scar himself?
It's a type of scarring called 'Crocodile Scarring'
The men of the Chambri tribe in the East Sepik province of PNG practise crocodile scarification, an initiation for boys entering manhood during which their skin is cut and scarred to represent the scales of a crocodile. The crocodile is a significant spiritual and symbolic animal in PNG, and the Chambri tribe believes it descends from the powerful predator. The ancient myth tells the story of how crocodiles migrated from the Sepik River onto land to eventually become humans.
If you want to learn more watch this documentary by the National Geographic on it.
How many scars does he have?
Well we don't know that for certain but an interview with Michael B Jordan himself stated that (according to Bleeding Cool)
“Ah man, it was something like… I wanna say it was something like maybe 2,200 or something. It was a few of them. We had a couple bets to figure out exactly how many was in there. But I can’t remember exactly, the number.”