Travel to Pointe Verdun to look for Burke at the marked Dive Bar. Head to the back door to trigger a cutscene. After that, hop on his ride to start the Drive like a Madman sequence to impress Burke. If you already caught up with an escaping informant while he is attempting to escape, then you should be familiar with this stunt.
The easiest way is to drive into incoming traffic and hit a few cars as well. Make sure you don’t leave the district to avoid failing the mission. Doing the dangerous stunts will increase the gauge on the top of the screen and slowing down or doing nothing will slowly deplete it. After filling the gauge completely, Burke will ask you to stop and get out. Mission complete.