A protest leader acknowledged in an Internet post that she took down the Sheriff's Department flag from in front of the County Jail and burned it at Miller Park.
Marie Mott said she did so because "I got tired of seeing it flying knowing there are black, brown and poor white people in that jail while white people are allowed not to wear a mask when we have a virus that kills people."
Authorities said an American flag was also pulled down and was found in some bushes.
Cameron Williams, the other main protest leader, is shown in video igniting the fire.
Chattanooga Police said they were not looking into the case.
Ms. Mott is a candidate for the City Council seat held by Anthony Byrd.