Will the 15 in. x 23 in. Galvanized Steel Adjustable Flue Guard Chimney Cap Spark Arrestor work when the chimney flue does not stick up above the brickwork?

Here is some information about the Adjustable Flue Guard Chimney Cap Spark Arrestor

Yes. Just make sure that it sits flat on the brick of your chimney and that it is securely attached.