During the Gain New Allies main story quest, you will be kidnapped and appear in the camp of the Elven Kingdom, where you are first introduced to Kyle, the Elven King. Talk to Jimmy here to initiate this quest, then make sure that he is set as your Buddy. Once he is, head to the farm in the upper right corner of the map.
When you get there, a cutscene will occur and Rancher Bill will give you the keys to the barn to take care of the Nazi Zombie Cows. Their only attack is to explode and kill themselves, so make sure you block the attack, since all four will likely kill you if you don't. After the battle, climb the ladder, shoot down the lantern and use a fart to clear the path to the chest with the Flute. Return to Rancher Bill to finish the quest.
