Born a dumb horse in England, Fledge was originally named Strawberry. His sire was an officer's charger in the English cavalry. His owner, Frank the cabman (later Frank I of Narnia) used him to pull a Hansom cab in London.
In 1900, while he was at work drawing his cab, a strange woman suddenly took him from his owner, and began whipping him harshly, forcing him to quickly gallop through the streets of London. They came to a stop, though, when the woman, Jadis, crashed the cab into a lamp-post. However, Jadis had by then leaped onto the horse's back, and said some things to madden him, causing him to start galloping on.
Eventually, they were stopped by the police, and Frank tried to calm him down, while trying to get Jadis off him, only for her to call him a dog, and that Strawberry was now her Royal Charger.
While everyone was trying to apprehend Jadis, Digory Kirke and Polly Plummer grabbed hold of her heel, and transported them all to the Wood between the Worlds. But because everyone had been touching one another at the time, they had also accidentally transported Strawberry, Frank and Andrew Ketterley into the Wood with them as well.
In the Wood, because he was thirsty, he wandered to the nearest pool of water, pulling the rest of the party with him, and attempted to take a drink. The pool was a portal to the newly created world of Narnia, and the whole party was transported there. Thus Strawberry was the one who first (accidentally) chose Narnia as a destination world, starting all contact between Earth and Narnia.
During the creation of Narnia, Strawberry was chosen as one of the first talking beasts by Aslan, giving him the power of speech. This allowed him to tell his former owner, Frank, how unpleasant his life as a cab-horse had been.
Later on, to carry Digory and Polly on their quest to find a magical Silver apple tree, Aslan again chose Strawberry for a special transformation, this time giving him wings and renaming him Fledge, the Father of all Flying Horses.
The newly changed Fledge flew Digory and Polly into the Western Wilds of Narnia, to the walled garden to pick a Silver Apple for Aslan, and then brought them back.
Strawberry lived the rest of his life free in Narnia, and his cab-man became King Frank the First.
Fledge made a cameo in The Lion, the Witch and the Wardrobe in the 9th Chapter of the story, In The Witch's House. While walking down the corridor towards The White Witch, Edmund points out there is a winged horse turned to stone, pointing to Fledge being one of a kind in Narnia.