If you very gently stroke from under his chin down towards his chest with flat hand, you will stimulate his swallow reflex. When it comes down to it, he has to take it, so sit down with him, hold him still, put the syringe at the back of his molars on one side and do it quickly, close his mouth and stroke his throat a couple of times. He won't be able to help swallowing it. Then a glass of juice or something he doesn't usually get to have, lots of praise and distraction.
After 3 days of bargaining, negotiating, bribing, encouraging, explaining, pleading and chasing DD1 around the house wasting antibiotics, this was the only way we could get it done. After a couple of doses, she realised that she was going to be given it whether she likes it or not, and it was much easier.