Chimney-sweeping was a dangerous job, and there was little joy and a lot of suffering for the children involved. Blake talks about how Tom's head was shaved (which made him cry). All the sweepers in the dream are "locked up" in coffins, the speaker was sold by his father, and the only place the children get to play and be children is in Tom's dream. Yep, there's lots of suffering in "The Chimney Sweeper." The sad thing is it's the children who bear the brunt of it, and there's no end in sight.
The poem argues that resurrection and rebirth can only happen after one has suffered. The children can only wash themselves and rise on clouds after they've been locked up and covered in soot.
The suffering in this poem is a result of society's cruel indifference, as represented by the angel's lesson: do your duty and it'll all be fine. Shmoop's left foot.