That depends on what kind of zombie you’re talking about. Voodoo zombies are either corpses brought back from the dead, or live people who’s souls are being controlled by a sorcerer. In this case, essentially, you use the person how you will. You control them. If they are, or were, a pilot, I imagine they could fly a plane if you commend them to. Voodoo zombies that are corpses would have to be fresh enough to physically be able to fly the plane I imagine, but what they knew in life is yours to command. I suppose you could get a zombie that has never flown a plane before to do so, although without the knowledge to fly it, it would be pretty unsuccessful. Voodoo zombies have no will of their own, so it’s unclear to me if they would be able to go where you tell them to with the plane, unless they already knew where that place was.
See here for folk/voodoo zombie information. Early zombie movies all deal with the voodoo type, showing people using them as mindless soldiers in war and stuff, but I’m unsure of the distinct difference between actual folklore and legend as opposed to what they show in the movies.
If we’re talking about the modern Romero type zombie that eats the flesh of the living, it’s absolutely impossible for them to do anything like flying planes. Those types are constructed with the idea that they do nothing but seek the living, eat them, repeat. Although some movies show them sometimes acting slightly human, learning to open doors or use blunt objects to attack, something as complex as flying an airplane would never happen with either shamblers or sprinters, even if they were pilots in life. It is very clear that they are run by instinct, and will answer to this, and this alone. The zombie’s brain is the motor, and Romero suggests that only a small part of the brain is responsible for that, while the rest is dead. Which makes no sense if the zombie can sometimes make a small link to objects or people which has nothing to do with instinct, but those are movie only zombies. (which means it’s free to exception; some zombies talk, use firearms, drive cars) At least I’m not aware of any actual folklore or legend that includes flesh eating corpses. Anything I find about that are living humans who practice cannibalism, or other creatures/monsters that don’t fit the definition of ’‘zombie’’.