Horse flicking head when cantering

Sounds like the bit is displacing in his mouth, or he needs a martingale to keep his head down. What else is he doing while cantering ?

Tick

You may have too much of a contact with the horses mouth. Keep a contact but try softening your hands by turning your thumbs to the outside so your fingers are facing upwards. Also maybe try a softer bit and check that your bridle fits correctly. If not then try using a running martingale to keep the head down.

I hope this helps :)