I have learnt they are the fundamental elements of Aristotle's categories and they are represented on south korea's flag. Seems just a little bit coincidental.
Eastern philosophy (specifically Taoism) uses 5 elements rather than the 4 in the west. It is composed of fire, earth, water, wood, and metal, which is quite different so I would conclude that they were not independently developed at all.
Furthermore, what you think of as wind (as represented on ROK's flag with 3 solid lines) is not correct. It represents the concept of heaven (or sky) which seems like it is analogous with wind or air, but it is more close to the concept of change which is in contrast with the concept of earth which is the unchanging.
In typical Taoist symbolism, there are eight different trigrams. The four that were chosen represents opposing forces (earth vs heaven, water vs fire). The flag is all about representing balance, which is why these symbols are places on opposing corners as well.
Hope this helps.