Peggy:
I think mris_reverse will do the trick.
But one cautionary note... I think when I investigated this there is a minor problem.
The job of mris_reverse is to flip the sign of the RL coordinate on each of the vertices, and also to change the order of the vertices in the sets of three points that make up each triangle (because order of the three points is used to indicate "inside" and "outside" the brain).
If you wish to have your flipped surfaces viewable in conjunction with your original COR volume you might be tempted to flip the input volume also (using for example AFNI or some other MRI software).
However, 0,0,0 in the coordinate system used by FreeSurfer is not in the center of the COR volume, it's off by half a voxel. Ie: in the L-R direction, the center of a COR image (ie: between the two middle pixels) is at R = 0.5 mm. [*]
The net result will be that the flipped surfaces will misregister with the flipped MRI volume by one voxel RL (ie: half + half).
For some users this is no concern at all, for others its a problem.
More details at:
http://wideman-one.com/gw/brain/fs/coords/fscoords.htm
Graham
[*] Subject to the usual possibility of getting off-the-top-of-the-head details wrong in emails.