Brick is a very porous material. Many paints and coatings “soak in” to brick or concrete, and this can make them difficult to remove. If the paint is primarily on the surface, a good scrubbing with a mildly acidic cleaner works best. But if the paint has penetrated, you will have to do a heavy etching with muriatic acid to remove it. Working with Muriatic acid can be dangerous so make sure you read all the instructions so you don’t hurt yourself or the bricks.
There are some specialized coating removers that come in a paste form that work well for this type of application, but they are not widely available at this point in time. The Hydrostrip line from ICI or a product called Masonry Strip available from Napier Environmental Technologies are the products to look for. They are also sold under the Biowash.com brand name found in paint stores like Sherwin Williams, Cloverdale Paint, and major home centers like Home Depot etc. check www.Biowash.com for a 1-800 to locate the product near you.