To Kill A Mockingbird, Chapter 3: Describe the type of chores that Burris Ewell may be responsible for at home.
After her first day at school, Scout relates what has happened to her father. When Atticus learns of the behavior of Burris Ewell, he tells Scout that the Ewells "had been the disgrace of Maycomb for three generations" because none of them had ever done "an honest day's work." They live near the garbage dump and are filthy; their father drinks on the welfare checks he receives. He hunts whether it is the season or not, and people do not report him because they know that his children would be even hungrier if Ewell did not procure game.
Since not one of the Ewells work and Bob Ewell, the father, is often absent from the home, there are probably no regular chores that Burris performs. Perhaps, he goes to the dump and finds whatever the family can use. He may fetch water if the family has an outside well (although he apparently does not bathe), and he may be big enough to shoot a .22 rifle (or set traps) and kill some wild rabbits or squirrels for meals.
Burris Ewell is the son of Bob Ewell, who is known to never be at home.
Robert (Bob) E. Lee Ewell, a cocky, uneducated widower who spends his relief checks on green whiskey and lets his oldest daughter, Mayella, worry about how to feed herself and the other seven children from what she can forage from the town dump. After Atticus implies in court that Bob, not Tom, beat Mayella, Bob vows revenge. He is found dead with a knife in his ribs after Scout and Jem are attacked.
Considering Bob Ewell's character, you know that he leaves the children home to do the housework and to support themselves. Since Burris is a male, he probably did a lot of the physical labor that Mayella couldn't do, like deal with the lumber or get water from the well, hunt for food, etc.
Miss Caroline sees a louse on Burris and becomes hysterical. Little Chuck Little tries to smooth things out.
This quote also shows that Burris is probably often outside and dirty.