I have made no prior research into this so this is all just observation. But, given how similar flag and banner designs were (and they still are) how did places come up with designs that were unique to them? Was there some kind of reference one can look at? How was this reference updated? Are there instances of two places having very similar or exactly the same designs?
I can answer for coats of arms, at least.
Duplication of arms was entirely possible. If the conflict was found at a tournament, the kings of arms (the heralds in charge of the tourney) might adjudicate, and require one of the men to difference his arms, at least for the duration of the tourney. In an army, the officials of the army might be able to make a similar judgment. Some areas had a permanent king of arms, appointed by the king or other authority, or someone else, who had authority to judge cases of arms. In England, it was eventually Garter King of Arms; in Scotland, it became and still is Lord Lyon King of Arms.
A famous early case is Scrope v Grosvenor, both bearing "Azure, a bend Or" in an invasion of Scotland. The Constable of England first heard the case, and required Grosvenor to add a difference (the difference added was a white bordure). Richard II heard the appeal and required more difference, so Grosvenor changed to "Azure, a garb Or", a completely different item on the shield. But the separate case of Carminow was judged differently: Cornwall was deemed to be a different nation.
(As an aside, I've heard that Scrope was politically important, so he wasn't allowed to lose the first case. But Carminow "proved" that his family had borne the arms since King Arthur (completely impossible), before Scrope's family's "proofs", so declaring a separate jurisdiction was the only way to get Scrope out of trouble. But this is hearsay, so I hesitated to even mention it.)