It’s not absolutely necessary to watch Captain America: Civil War before Black Panther, but it does help with following along with T’Challa’s personal journey and comparing him to Killmonger.
After T’Chaka was murdered in Captain America: Civil War, T’Challa tried to kill Bucky Barnes, who was originally believed to have carried out the bombing.
In sharp contrast, Nate Moore mentioned during his appearance on The Empire Film Podcast that Killmonger probably would have killed Zemo instantly.
He was never able to effectively cope with losing his father at a young age, which resulted in him becoming the villain we see in Black Panther.