When two vehicles are coming towards each other and both are turning right, no one should have to give way.
This is because normally neither will cross the other's path, so both vehicles can turn safely. However, be careful if the other vehicle is a large truck or bus, as they may need more room to make the turn.
Remember to check for traffic coming towards you that is going straight through the intersection (see The give way rules). Your view might be blocked by the turning vehicle.