Hold the mounting plate of your wall mount to the brick wall on your fireplace. The mounting plate is where you will attach the TV and is included in the wall mount kit. Select an area where you want to hang your mount. Use a level to make sure it will be straight on the wall. Mark the mounting holes' location on your mounting plate.
Mark the location of your mounting holes on the brick with your pencil, using your measurements. The ideal location places the mounting holes at the center of a brick, because mortar is weaker than brick and drilling into a brick's corner can cause it to chip.
Use your masonry attachment to drill your mounting holes, based on the marks that you made with your pencil. Blow the dust and debris out of these holes, and apply glue to the outside of your wall anchors to insert the mounting holes.
Line your mounting plate's mounting holes in the wall anchors and secure your plate to your brick wall. Do this by inserting the screws through your mounting holes and into your wall anchors.
Get your VESA-compliant screw holes from your mounting kit and line these up at the back of your flat-screen TV to the VESA holes in your mounting template. VESA stands for Video Electronics Standards Association and they provide specific guidelines in mounting TVs. Insert your VESA screws through your VESA holes right in the mounting plate, and into your TV's VESA holes. Have someone hold the TV while you screw in the VESA screws.