The Wonderful Wizard of Oz
The Flying Monkeys would appear to whoever wields the Golden Cap that was made by Princess Gaylette to bind their servitude to it as their punishment for their pranks. The Golden Hat's magic must be used three times before it can be passed on to the next person. The Wicked Witch of the West came cross this hat and has used it to help her take over Winkie Country and repel the Wizard of Oz's army.
Following the melting of the Wicked Witch of the West, Dorothy claimed the Golden Hat and asked the Flying Monkeys to take them to the Emerald City to present proof that the Wicked Witch is dead.
As the Flying Monkeys can't leave the Land of Oz after the Wizard of Oz's balloon takes off without her, Dorothy used up a command. The final time she uses it was to cross the hill of the Hammerheads in order to get to Glinda's castle in Quadling Country. When Glinda uses the hat to have them take Scarecrow, Tin Man, and Cowardly Lion to their respectful places, she gives the Golden Hat to the Winged Monkeys to destroy it so that they will be free of it's enchantment.
The Wizard of Oz (film)
In the film, one Flying Monkey was seen with the Wicked Witch of the West as she plans to obtain the ruby slippers that Dorothy wears.
When the Wizard of Oz sends Dorothy Gale, Scarecrow, Tin Man, and Cowardly Lion to bring him the broomstick of the Wicked Witch of the West, the Flying Monkeys are dispatched to bring Dorothy and Toto to them.
In LEGO Dimensions, a Flying Monkey can serve as a mode of transportation.
The LEGO Batman Movie
In The LEGO Batman Movie, the Flying Monkeys join the Wicked Witch of the West into being among the inmates of the Phantom Zone. When The Joker pitches his plan for them to attack Gotham City, one Flying Monkey tells them to get on with the plan after a Swamp Creature still considered Joker's story to still be boring.