Stay in a circle on the left at trot with a jump that's to about half of his cannon bone and you trot in circle on it, if he doesn't pick up a canter you raise it slightly.
He will pick up canter by using the jump as a starter.
When you go over the little jump ask for canter with your voice and repeat.
Once he has cantered, after two or theee strides you take him back to trot and stroke him and then repeat. You will soon need a smaller jump then a pole and then you will have a perfect left lead canter start.
I've used this with horses with damaged tendons who only cantered on one side to compensate and after healing didn't want to canter on the healed side.
Racehorses are taught from the start to only pick up the right lead out of the gate, then they lead change around the turn. It's not that he is unable to are maliciously intending to, its that all his life he has been trained to only pick up the right or he will have to keep redoing it until he only picks up the right. When asking, you can attempt to get into a 'jockey' position, which helps on some horses. Meaning put your weight onto your hands on the horses withers, and get off their back, then when in a corner maintain your center of balance and ask him to pick it up. This will work for some, if it doesn't, then try to use your weight and seat. Position yourself as though you were about to skip forwards, do not look down at the lead and instead look directly ahead, and put as much weight into the outside stirrup as possible. This will lean their bodies so it is easier to engage the correct lead.
We had a horse like that as well. What worked for him, was keeping him extremely straight in the transition. Don't let yourself tip forward and try not to let your hip or shoulders fall in. If he will do the flyings, just try and make the switch from right to left really efficient so that he starts to understand that you want him on the left lead, and that it would be much easier for him to pick it up originally. Practice in this case scenario will really help you. Just be really consistent in your aids, and give him lots of praise when he does what you want!!