Mapping the Left and Right Sides
This step should be trivial. If I remember correctly, the CMU database animation skeletons have easily identifiable bone names. If not, then it's slightly less trivial. What you would have to do then would be to start at the root and go down each side. The bone structure should be the same for each animation though.
Create the Rotation Matrix
You should have three Euler angles: $X$, $Y$, and $Z$. You first need to create a rotation matrix for each bone. I use $\phi$ for $X$, $\theta$ for $Y$, and $\psi$ for $Z$ since this is a more common notation for matrix $R$. This is a right-handed matrix.
$$
\begin{bmatrix}
\cos(\theta)\cos(\psi) &
\cos(\phi)\sin(\psi) + \sin(\phi)\sin(\theta)\cos(\psi) &
\sin(\phi)\sin(\psi) - \cos(\phi)\sin(\theta)\cos(\psi) \\
- \cos(\theta)\sin(\psi) &
\cos(\phi)\cos(\psi) - \sin(\phi)\sin(\theta)\sin(\psi) &
\sin(\phi)\cos(\psi) + \cos(\phi)\sin(\theta)\sin(\psi) \\
\sin(\theta) &
- \sin(\phi)\cos(\theta) &
\cos(\phi)\cos(\theta)
\end{bmatrix}
$$
Flip the Sides
To flip the rotation matrix, you will need to multiply the axis you want to flip by $-1$. This is equivalent to scaling in across that axis. I will assume you want to scale across the x-axis for matrix $S$.
$$
\begin{bmatrix}
-1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
$$
Combine the Two Transforms
Now just multiply these two matrices, and you get the opposite rotation:
$$T = R \times S$$
Chain Together the Local Transforms
Now you just need to apply forward kinematics, so you need to multiply each parent matrix by the local matrix to get an absolute transformation matrix.
