“Satan” appears only three times in the Old Testament, and only here as a proper name. The story raises so many questions. Whose actions initiated this story? Samuel says the Lord’s anger burned against Israel and he incited David against them. So there, it looks like Israel sinned and God was looking for an occasion to punish them.
But here, it appears that Satan incited David to take a census of Israel, God became angry, and took out His anger on His people – not exactly fair of the Lord.
But there is another way to look at the story:
As David sees God’s punishment of Israel, he begs for the judgement of God to fall on him, the shepherd of Israel. They are but sheep. He is responsible for them.
I think this speaks more to the point of the story for the Chronicler. Satan is operative and influences all Israel – including David – for evil. Israel’s sin is unspecified. David’s is that he took a census to see how many fighting men he had. What difference did it make? God would provide the necessary soldiers, or just sent the heavenly host. David was not just counting Israel; he was counting on himself.
You see a precursor to the destruction of Jerusalem by the Babylonians, the sword in the hand of God. But God is gracious, and did not completely destroy His people.
There are at least two points here: First, God is in control.. He can use anyone or anything – including Satan – to accomplish His goals. Second, the leader of God’s people sets the standard for His people. When he sins, the people follow. They will never be more righteous than their leadership.