Officers said the SUV's plates indicated it was actually a stolen motorcycle.
"They don't deserve to wear a badge anymore," Aurora's interim Police Chief Vanessa Wilson said.
Jones and two other Aurora, Colorado, officers reportedly mocked the police killing of McClain, a Black man who was walking home last year.
Some family members of the victims are also calling on Warner Bros. to support gun control measures.
Tom Sullivan, the father of one of the 2012 theater shooting victims, introduced the Democratic presidential candidate at a rally on Thursday.
Mayor Michael B. Hancock said his son's response during a traffic stop was "inexcusable."
The campaign was launched by the parents of a victim of the Aurora, Colorado, theater massacre.
"To get through my PTSD, I have to accept that I’ve been shot and that my life has been completely altered."
Joshua Nowlan, 36, Aurora, Colorado. Aurora theater shooting, July 20, 2012. Joshua Nowlan worked at a cinema advertising
Heather Martin, 36, Aurora, Colorado. Columbine High School, April 20, 1999. Heather Martin spent hours trapped in a small
"I remember feeling really scared that he could be around any corner, because we weren’t sure exactly where he was."
Chelsea Sobolik, 29, Fort Collins, Colorado. Aurora theater shooting, July 20, 2012. Chelsea Sobolik had just come off a