First, a negative demonstration in the left diagram: Red is too quick to make two successive checks, and soon finds himself at wit’s end. The correct approach leading to the Staggered Chariots checkmate is shown in the right diagram.
Never overlook the Cannon’s ability to protect the King from behind. The second check indeed helps Black to get his King out of danger. After that, it is Black’s turn to start the offensive and he wins eventually.
The first check is necessary, to prevent Black from moving his King to safety with K6=5. The 2nd move is the key winning move, which stops the King from going to the palace top and taking cover with the Cannon at the other wing.