Warm or Cool
Because red is a warm color and gray is often perceived as a cool color, the biggest problem when selecting a siding color for them is whether to choose a warm color or a cool color. Warm colors may blend with the red brick but not the gray roof, and cool colors may be blend with the roof and not the brick.
In general, the solution is to match the roof. Red brick is so common that people perceive it, like blue jeans, to be more of a material than a color.
Bluish gray, or blue-gray, is a cool enough color to work well with a gray roof, and it creates a pleasant contrast with cooler shades of red brick. It shouldn't be paired, however, with a very warm shade of red brick, such as red-orange brick.
Bluish gray goes best with darker shades of red brick that contain no overtones of warm orange. Combine bluish gray with white shutters, white trim and a rich red door to match the brick.
If the red brick is a particularly warm shade, then siding that is a cool brown is an option. Cool browns have a lot of gray in them, and they mix well with red brick and a gray roof.
Combine cool brown siding with white- or cream-colored trim and a dark brown front door.
Unfortunately, white isn't the most interesting color to use in decorating. It's harsh and bland.
White siding, however, goes with a gray roof and red brick just fine without clashing. If you can't find a siding color that makes you happy, then white may be the solution.
If you're worried about its blandness, add splashes of color to the house's exterior. Trim, shutters, landscaping and exterior doors all present opportunities to add color to your house.