I think it makes sense that he wants the money for reasons like paying his men their dues, purchasing weapons, explosives, vehicles, paying off cops, etc. The money he steals at the very beginning however is the $61 million that Maroni and company talk about in the kitchen meeting scene, and I think Joker steals that to make a point to them that he means business and isn't afraid of them.
I think he asks for half of the money as a show of power. He could care less about the money himself, what's important to him is showing them that he is the one who is in control, and when he says he wants half of the entire pot to himself, they better do it. And they do. But that's all that it means to him: the doing of it. So he burns it.