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
.