Where would you put the saddle? On the neck or on the hip?
Thanks for the answers and comments.
The prime spot would be between the wings with the legs draped over and in front of the wings, straddling the neck.
I'd use a "flat harness", i.e. the animal wears a harness that holds the rider lying flat on the animal's back. This would minimise air resistance and lower the rider's centre of gravity, which would make it easier on the griffin or drake, and make the rider much harder to knock off.