If A is a skew-symmetric matrix and AB' + BA' = 0, then BA is:

A matrix $M$ is skew-symmetric if its transpose is equal to its negative, i.e., $M^T = -M$.
We are given that $A$ is skew-symmetric, so $A^T = -A$.
We are also given the equation $AB' + BA' = 0$. In matrix notation, $B'$ refers to the transpose of $B$, so this equation is $AB^T + BA^T = 0$.

Substitute $A^T = -A$ into the equation $AB^T + BA^T = 0$:

Rearrange the equation to find a relationship between $AB^T$ and $BA$:

Let $X = BA$. To determine if $X$ is symmetric or skew-symmetric, we need to find its transpose, $X^T$.
Using the property $(MN)^T = N^T M^T$:

Now, substitute $A^T = -A$ (since $A$ is skew-symmetric) into the expression for $X^T$:

From Step 2, we established that $AB^T = BA$. Substitute this into the expression for $X^T$:

Since $X = BA$, we have $X^T = -X$.

The condition $X^T = -X$ means that $X$ is skew-symmetric. Therefore, $BA$ is skew-symmetric.

The correct option is B.

The final answer is $\boxed{\text{B. Skew-symmetric}}$.