Flight as a mode of transportation is fairly rare, and can be divided into two categories. Flight via flying creatures, and flight via magic.
There are quite a few creatures capable of both flying and carrying a rider at the same time. Unfortunately, these creatures are either sapient or hard to tame and train. And even if they can be trained, they will only accept the person who actually trained them as a rider (though some of them will accept other passengers as well). Thus, the availability of flight as a personal mode of transport is limited to those who spend lots of time caring for and training their mounts - not to mention deal with the difficulty of acquiring such a mount in the first place! Many elves have proven willing to do so, but among other races only few organizations (often but not always of a military nature) have been willing to spend the time and effort for such an enterprise. Most humans would rather save the time and effort and just travel where they want to go by rail and coach. It might not be as flashy, but it gets the job done - and ultimately costs less time and money.
That magic is capable of granting flight has been known for a long time, and many wizards enjoy flaunting their abilities in front of others. However, such spells require a lot of time and effort to learn - thus making them expensive - and only rarely last for long enough to get to distant locations, which means that more conventional modes of transportation have proven more efficient under most circumstances. Magic items capable of granting flight for longer periods are known, but thanks to the expense required in creating them, they are usually kept in secure locations instead of being casually used for other travelers, since the owners of such items don't want their investment stolen at the next opportunity. Instead, they are only used in emergencies or when they can be sure that no stranger will get hold of them. Thus, their impact on transportation is limited as well. Some ambitious artificers dream of flying golems who will usher in an Age of Flight when traveling through the air becomes affordable to the common man, but as of now, these remain pipe dreams.