Depending on your trivia knowledge, estimating the mass of the Empire State Building can be difficult. Here is my attempt:

I know the Empire State Building has around 100 floors. If I take the average height of one floor to be 4m, then the building is 400m tall. I’ll also guess that the average width and depth are about 50m each. That makes the volume about 400×50×50=1,000,000m³. If the building’s volume is about 80% air and 20% substance, then the volume of actual “building” is 200,000m³

I’ll guess that the Empire State Building is made of primarily reinforced concrete, and that the density of this reinforced concrete is three times as dense as water or 3000kg/m³, and thus the mass of the Empire State Building is around 600,000,000kg, and its weight is 6,000,000,000N (taking “g” as 10N/kg).

If the average mass of a pigeon is 0.5kg, and it can produce a thrust equal to its own body weight, then each pigeon exerts 5N on the building.

Therefore, you would need 6,000,000,000/5=1,200,000,000 or 1.2 billion pigeons to lift the Empire State Building at constant velocity.