Assuming the world in question to be of similar size to ours, same proportion of atmosphere etc. but whose surface is perfectly flat, and has a 0 degree axle tilt what sort of weather/wind current patterns would be produced?
The flat surface has little to do with the global air circulation since it is manly driven by the difference of air pressure caused by the global circulation of air itself and the difference of temperatures as well.
Having no tilting means there is no seasonal variability in the wind patterns and logically no season variation of temperature. A different wind pattern will affect the precipitations. Places that are wet will always be wet and places that are dry are always dry (places affected by a high pressure system like India during most of the year except in summer). For example, the Mediterranean climate could not exist since there would be no dry season in the summer. The monsoon would never occur in India because the the Sun would not be able to heat the land enough to cause the pressure to drop and thus change the wind to flow inland. Therefore, most of India would be something between a steppe and a desert.
One quick way to get an idea of what the weather would look like would be to look at temperature/precipitation maps for the month right after the equinoxes. This is because the most important factor is the energy received from the Sun.
In the Earth global wind circulation is heavily affected by geography - in part due to some topographical obstacles, in part due to different heating of continents an oceans and in part due to different transport of heat by different oceans. If the Earth were flat and oceans were uniformly distributed, global circulation would be the only factor with no local disturbances. Furthermore, without axis tilt there wouldn't be seasonal differences.
Therefore, in an uniform untilted Earth we could expect nearly constant winds, always eastward or westward according to latitude.
Earth Global Circulation (credits here).