How could one of the major organizations within the federal government most effectively overcome the Supreme Courts ruling to allow the federal government to outlaw flag burning

The correct answer is letter C. When the Congress wants to overrule a decision made by the Supreme Court, which could or could not have been previously said by the law, the Congress can simply change the law and make things clearer, or even create a new law or ammendment so that the Supreme Court could then have a law basis to rule.
c. congress could propose a constitutional amendment that would outlaw flag burning.