Is there an action for when permalinks are rebuilt?

The action is update_option_permalink_structure. You get the old and the new value as parameters.

add_action( 'update_option_permalink_structure' , 'my_custom_function', 10, 2 );

function my_custom_function( $oldvalue, $_newvalue )
{
    // do something
}

There are also the actions update_option_category_base and update_option_tag_base.