I got the impression that Gorkon was a rather populair Chancellor, and under his rule things started to change already. If Chang had won in a duel, a lot of people who supported Gorkon's ideas of improved relations between the UPF and the Empire would not support Chang and his visions for the Empire. He realized this all to well.
What he needed to do, was re-affirm the Federation as an enemy of the Empire. Framing one of the Federation's greatest hero's, James Kirk, for the murder of Gorkon (who was appereantly quite open for better relations between the Empire and the Federation) would make sure the Empire would rally against the UFP.