We recently had an addition put on our house. As part of the process, the contractor removed the portion of the chimney that extended through the roof. We had him carefully remove the bricks, breaking as few as possible. We're going to reuse the bricks (cutting them in half because we don't have enough) to use as a veneer on the concrete block foundation wall of the new structure so that it'll match the brick foundation of the rest of the house.
You could use the bricks in a structural wall, as a veneer, as a walkway, or sell or give them away for others to do the same, as well. If you use them yourself, you'll want to chip off as much of the old mortar as possible so that you've got nice even bricks to work with again. If you get a little aggressive and accidentally remove some brick with the mortar, just put that side in so that it doesn't show.
It wouldn't even matter if the bricks were used in a structural wall, as that won't make any difference to the brick one way or another. The only limit to their ability to be reused is whether they're broken, damaged or smoke damaged. Even if they're smoke damaged, that's probably only on one side and the other side will be just fine.