You can probably pull this into a reasonably flat state while fixing it to the wall as follows:
Drill and rawl-plug a row of, say, 2" no. 10 countersink screws into the wall where the convex rear face of the board is maximally warped (i.e. about half-way up the board height). Before fitting the board, screw these screws in until the top of the head is where you want the rear board face to lie. Get them all to the same horizontal line (unless the wall is curved!) by running a string along the row and adjust till they all just touch it. The heads should also lie on a vertical level with the finished wall surface. Note that these screws do not go THROUGH the board!!
The next step is to fix the board with pairs of screws, one above and one below each of the above screws. Then you should be able to pull the board flat as you screw it to the wall with these screws, bearing against the first row. These screws need to be fairly substantial and properly rawl-plugged into the wall, again 2" no. 10 countersinks should do.
Be careful as there are a few "gotchas". The main one is the problem of rawl-plugging the screws behind the board so you can pick them up later with the screws. The only way to do this is to drill pilot holes through the board at all locations, then offer up the board to the wall and pass a masonry drill of the same diameter through these pilots to 'pilot' the brickwork behind, then remove the board and finish off the holes to final rawl-plug size. You can countersink the board at this time. Now when you finally fix the board the screws should find their rawl-plugs OK.
Another "gotcha" is that you may find some screws falling into voids between the bricks. You need to check that the intended screw positions do not fall into these. Also you have to be careful not to put the top screws into too thin a section or you may split the board.
If the board is warped the other way (convex) the procedure is similar, but you put two rows of supporting screws behind the board and fix it with one row along the centre line. In either case there are 3 screws at each fixing point.
Its rather complex to achieve, but this method results in a perfectly straight and vertically fixed board. The downside is that you have to fill over the screw heads before decorating. To locate the screws for subsequent board removal - use an electronic cable/batten/pipe detector.
-- Phil Addison The uk.d-i-y FAQ is at