Why did Trevor and Blackie burn Old Misery's money instead of just keeping it?

Your question relates to the motivation of the boys for doing what they are doing. Repeatedly, the boys show that they aren't destroying Old Misery's house to steal or to do anything that they think is "illegal" from their point of view. Note what Trevor says to Blackie concerning the money:

"We aren't thieves," T. said. "Nobody's going to steal anything from this house. I kept these for you and me - a celebration." He knelt down on the floor and counted them out - there were seventy in all. "We'll burn them," he said, "one by one," and taking it in turns they held a note upward and lit the top corner, so that the flame burnt slowly toward their fingers.

A word that strongly defines the attitude and motivation of Trevor is nihilism. Trevor just doesn't care about the things the world finds valuable, and this is perhaps a further example of Trevor's philosophy of life. Also, we can infer from Trevor's family background that since his parents have gone down in the world, burning Old Misery's money rather than stealing it is another form of sending a message that he rejects the values of the world. This is why it is a special "celebration" that Trevor shares with Blackie alone.