The video, posted in 2019, shows military dogs attacking a man in Colin Kaepernick's San Francisco 49ers jersey during an event at the Navy SEAL Museum.
The scripted limited series “Colin in Black & White” will explore the athlete and activist's formative high school years.
The NFL commissioner said he supports the quarterback resuming his career.
In a tweet, the president stoked conflict after the NFL commissioner apologized for not listening to players who demonstrated against racial injustice.
The secretary of housing and urban development said NFL players should express their love for the military as they protest police violence. Players have already said they support the military.
One person mocked the president by saying, "The racism will continue until morale improves."
Brees' teammate, New Orleans Saints receiver Michael Thomas responded on Twitter, saying, "He don’t know no better."
The former Carolina Panthers safety referenced Colin Kaepernick's status in the league, writing, “I think you meant Blackball Tuesday.”
Charlamagne Tha God, the show's host, called Limbaugh "delusional" after his guest termed white privilege "a liberal, political construct."
“Colin Kaepernick asked the NFL to care about the lives of black people and they banned him from their platform," one sports writer tweeted.