The poems speaker, I feel, is interpreting a dream of a young boy he knows. He tells of having to work as a chimney sweeper to help support the single parent family he lives in. The speaker seems to have a very religious background because of all the belief he has in the angels coming and opening the coffins of the dead sweepers and setting them free to be in heaven together. I think that both young boys are missing having a complete family and look forward to the fact that if they perform their duties as chimney sweepers to the fullest that God will be their father and will complete their family.
The soot is representing the belief that the children are unfit to enter Heaven because they are so dirty. The dream consists of the children cleansing their bodies in the river to be free of the dirt so that they may enter heaven.
I also think that the child labor was very common and that these children were up to work early before sun up and worked very late into the night. The children did not complain about the jobs or the hours because they knew that if they did their work properly, they would have nothing to fear.
I think that as a reader, you tend to want to believe that as the poem states, the children would be rewarded greatly by the heavens if their work was completed. However, I think that we each know that the children probably all worked until they found themselves very health stricken and never got to enjoy the reward.