If there are voltage or potential difference, then the current starts to flow from high voltage to low voltage. But when a small bird sits on the power line, both feet are on the same voltage line!

Therefore, there are no potential difference between these two feet.

Let's say the power line is very low, almost touching the ground, and a chicken is trying to cross it. If one leg is on the ground and the other one is on the power line, then there are potential difference between these two legs.

Therefore, there is a flow of charge and eventually the chicken will be barbequed like the diagram above.