No need to do any math here.
One of Pongo's arguments is something like "Their migratory paths would be efficient on a flat Earth, but not on a round Earth." This is irrelevant; all Pongo's saying (whether he knows it or not) is that a flat Earth would be better for birds than a round Earth.
Pongo is correct when he talks about natural selection favoring those who are most efficient/adapt the best to their habitats. However, in this case, the shape of the Earth is irrelevant. Birds will adapt as best they can regardless of the shape of the Earth.
Another case Pongo makes is that birds fly at high altitudes, which is (insignificantly**) less efficient than if they flew at low altitudes; therefore, he says, natural selection would essentially kill them off. Yet they're still here, and he claims it's because the Earth is flat.
Yet there are dozens of other factors that influence the birds. They may fly at high altitudes to avoid predators, for better weather, for less dense air, etc.
This is all not to mention how insignificant the increase is in distance between flying at ground level 38,000 feet in the sky (the highest recorded altitude bird's flight): a trip around the (round) Earth along a longitudinal line at an altitude of 38,000 feet is only .3% more than a trip at ground level.
Not enough to kill off birds.
Radius of the Earth: 3963.1676 miles
Radius of the Earth + 38k feet: 3970.3645697 miles
Circumference of the Earth: 24859.82 miles (along a longitude)
Circumferenec of the Earth at 38,000 feet: 24946.536328 miles (along a longitude)