Safer cordite could not compensate for defeated flash precautions

Would the cordite rotation introduced after the loss of Vanguard have helped if it had been in place before Jutland?

It might have helped, but following magazine and flash-protection procedures mattered much more than propellant chemistry alone.

Newer, more stable cordite would have been useful, but correct magazine procedure mattered more. Leaving doors open to move ammunition and powder faster bypassed systems intended to keep a turret fire from spreading into the ship. Those systems could protect the rest of the crew even when men in the hit turret could not be saved. Propellant improvements could not restore safeguards that crews had defeated.