It's unclear why Death takes on the form of Black Flash to track down speedsters - though some theories are made that either top-rate speedsters (such as the Flash) are too fast for traditional Death to catch up with or that Black Flash is a result of some kind of anomaly caused by the Speed Force itself, whatever the cause Black Flash exists for one purpose: to end the lives of speedy heroes and villains in the DC universe.
It should come as no surprise that the Black Flash is an enemy of the Flash (both past and future-versions) but his appearances are fairly rare - as is the case for most personifications of death, after all the arrival of the Black Flash usually suggests that Flash is about to die or in serious danger of doing so. Though unlike most versions of Death the Black Flash is capable of being defeated or at least stalled so not all encounters with the entity need be fatal to a speedster, though a victory against a being like Black Flash is likely in vain as he will keep coming back until his job is done.
In Other Media
Smallville Season 11
The Black Flash first appeared to Bart Allen while he was being tortured by Lex Luthor for swiping corporate data from him in the episode "Justice". Lex forced Bart to run at super speed to avoid charged floor that would electrocute him to death. Bart discovered he could tap into the Speed Force just like that and immediately saw the dark creature waiting for him outside the glass. Black Flash tried to grab Bart after he passed out, however Bart was saved by Clark Kent. Years later, Bart told Clark about what happened and Clark decided to go to S.T.A.R Labs to seek Emil Hamilton's help. Professor Hamilton designed the treadmills to allow Bart to run as fast as he can while Clark's treadmill can accelerate him toward Bart's speed. The goal of this experiment was so that Clark can see the creature once he becomes fast enough. Bart tapped into the Speed Force and ran so fast that he caused the treadmill and the monitoring equipment to explode. Clark fell into the floor and saw Black Mask coming towards him. Black Flash decided to not drain Clark's speed since he didn't consider it to be pure and Clark vowed to help Bart stop him. Clark attacked Black Flash as he was draining the speed of other people in Los Vegas while wearing a new suit. Black Flash tried to kill him until Bart Allen sacrificed himself to stop the creature. Clark was then left mourning Bart's death.