Dunn, 19, died when his motorcycle collided with a car outside the U.S. military base in Northamptonshire on August 27, 2019.
Radd Seiger, the Dunn family spokesperson, said the video suggests "a new tragedy is inevitable."
Harry's mother Charlotte Charles and father Tim Dunn said earlier that they had seen "no evidence" of the government's review of his options after an extradition request for Anne Sacoolas was refused last month.
Sacoolas, 42, the wife of an intelligence official based at RAF Croughton, claimed diplomatic immunity and was able to return to his country of origin, triggering international controversy.
Charles questioned the Prime Minister’s leadership and the lack of action to bring his son’s alleged murderer back to the UK. She told PA Media that she felt her family had to drag the government "through a hedge back" to take action to do justice to the teenager.
His mother said, "It is so important to my family that no one suffers like us. I will not leave Harry's death in vain. I want his legacy to be that diplomats stay and face the consequences of their crimes and not be allowed to flee, that we get an ambulance when we need it and not when it is too late, and to guarantee the road safety. in and around the bases is greatly improved for both US personnel and local residents.
"You would have thought that these would also be important issues for the government, and they would take urgent measures to work with us and to sort things out and reassure people. But not a little. "
The video was released after Northamptonshire chief of police Nick Adderley met with U.S. Air Force Colonel Bridget McNamara on Thursday to discuss security.
A joint statement issued after the meeting said that McNamara had "provided a detailed summary of all the proactive steps the base continues to take to help people living on the base adjust to British standards of conduct."
Adderley said: "It was clear from the meeting that the base already had a number of measures in place to keep drivers safe." He described it as "encouraging" to see.
A "shocked" Seiger said the family was unaware of the meeting and "should have been there."