From a strictly technical standpoint, if the world is indeed flat then it will not be subject to the normal forces that affect the real world (such as the coriolis effect and hadley cells, etc.) that create the climate patterns we have here.

So... I'd start at the basics. Despite being flat, for instance, is your world roughly the same size as Earth in area covered? I know you say the seas are "infinite", but you also suggest that sailing off one end dumps you out on the opposite end of the world. Is that true both E/W and N/S, so that if, for instance, you sail too far north, you are suddenly in the south? If that's the case then your flat world is, in fact, being subject to some pretty interesting geometry.

Anyway, if the it's the same size as Earth, does one region still get more sunlight than the other during different times of the year? In other words, do you still get seasonal variations in temperature? (I guess this implies that in summer, the sun-god travels more over the northern sky and in winter more over the southern sky.)