They refer to it as 'border disputes'. Basically squabbling about little sections of land, much like what's happening with Israel and its neighboring countries right now.
So with the information given, they were at peace due to the last flame bringer war and both sides participating to stop Harmonia. Slowly border disputes escalated until they got so bad that battles broke out. Not 'WAR!!!!!' but getting there. So the beginning of the game shows the severity of those disputes with the Captain of the knights kicking the bucket. This is basically a plot point to build up how important the peace treaty they were about to sign was.
And for the record, kudos on your SIII avatar. Not the best one on the board, but a valiant effort nonetheless