The footage shows the high-speed chase from the perspectives of Effiong Nsa, Salah Ibrahim and Shamil Ibrahim after they attempted to evade police, having robbed a man at knifepoint in Dartford, Kent.
Nsa had pulled out a machete and told the victim to "give me everything you got", KentLive reports.
The victim tried to run away but was chased by the three yobs, who grabbed the back of his coat and pulled him to the floor.
He then handed over £20 to Salah Ibrahim.
The live stream shows the trio in the car, being driven by Shamil, who is driving recklessly, running multiple red lights and heading into oncoming traffic.
Salah, who filmed the live stream, also showed how the group appeared to be excited about the chase.
At the start of the clip, shouts of "live Fed chase" - referring to American slang for Federal Officer - can be heard as Salah appeared to imitate police sirens.
As the video continues, Salah can then be heard shouting "Oh my god.... swerve - swerve!" as the vehicle sped towards oncoming traffic.
Salah also appealed for viewers to come to their assistance, saying: "Need your help - get in your car, come help us block off the feds I beg you."
A spokesman for Kent Police said: "Officers located the BMW close to the location of the offence.
"It was being driven by Shamil Ibrahim, with the other three passengers inside, and failed to stop when it was requested to do so.
"A pursuit then took place, during which the vehicle was driven at excessive speed across Dartford, Swanscombe and Northfleet.
"It was also observed travelling through red lights, driving towards oncoming vehicles, and heading the wrong way around a roundabout.
"As the chase was ongoing, Salah Ibrahim live-streamed the offending on a social media account belonging to him.
"Despite their dangerous efforts to evade capture, specially trained officers were able to bring the getaway car to a controlled stop on the A2 coastbound.
"Effiong Nsa and both Ibrahims were then pulled from the car, with [co-offender] Sunny Reeve detained on the same afternoon elsewhere in Dartford."
The trio was later sentenced to several years in prison between them, with Nsa already on bail for a separate robbery offence at Bluewater Shopping Centre on August 29, 2020.
Nsa, 19, of Gravesend, admitted two counts of robbery, attempted robbery and possessing an offensive weapon. He was sentenced to four years and two months’ imprisonment.
Reeve, 23, of Dartford, admitted one count of robbery and was sentenced to two years and four months’ imprisonment.
Salah Ibrahim, 20, of Gravesend, admitted robbery and was sentenced to two years and eight months’ imprisonment.
Shamil Ibrahim, 21, of Gravesend, admitted dangerous driving. He was sentenced to four months’ imprisonment, suspended for a year, at Woolwich Crown Court on 5 May.
He was also ordered to complete 150 hours of unpaid work and banned from driving for 18 months.
