Fastest way to level up a griffin

Experiments

The experimentation table is one of the best sources of xp in the game. You can get millions of xp per day, the downside is it can only give enchanting xp, which means your griffin wont level up as fast as if you got combat xp, but it still helps a lot, its how i got my giffin to level 75. As a bonus, you can get xp bottles (all types) and enchanted books including tier 6 and 7 books (which are often worth millions).

Plain old grinding

Drink a combat xp boost (obtainable from gifts) and start grinding, I would recommend the end (crypts if you want to get rev slayer up).