@Onyx_Chess The way I would see it is like @Sarg0n says above - the game comes first, and then the clock is a secondary element that was introduced to ensure the game doesn't take forever. And the object of the game is to give checkmate - and so once this is done, the game is over, and this takes priority over the secondary element (the timekeeping).
So the rules are clear - checkmate takes priority and flag fall does not occur until pointed out by the opponent or the arbiter. But, yes, there will very occasionally be times when the opponent (or arbiter) calls 'FLAG!' simultaneously as the queen lands to give checkmate - and then it will be tricky to determine the result.
For some history - as far as I know this became established following the games Rumens-Mabb in the 1958 London Boys championship. It was the last round game with the result determining the championship. Rumens delivered checkmate but his flag fell after he moved but before he pressed the clock. The laws were felt ambiguous and the game ended up being referred up first to the British Chess Federation and subsequently to the FIDE committee on the laws of chess to determine the result, thereby establishing the precedent that still holds (checkmate takes priority, Rumens won).
For this history see
http://www.saund.co.uk/britbase/pgn/195801londonboys-viewer.html
So the rules are clear - checkmate takes priority and flag fall does not occur until pointed out by the opponent or the arbiter. But, yes, there will very occasionally be times when the opponent (or arbiter) calls 'FLAG!' simultaneously as the queen lands to give checkmate - and then it will be tricky to determine the result.
For some history - as far as I know this became established following the games Rumens-Mabb in the 1958 London Boys championship. It was the last round game with the result determining the championship. Rumens delivered checkmate but his flag fell after he moved but before he pressed the clock. The laws were felt ambiguous and the game ended up being referred up first to the British Chess Federation and subsequently to the FIDE committee on the laws of chess to determine the result, thereby establishing the precedent that still holds (checkmate takes priority, Rumens won).
For this history see
http://www.saund.co.uk/britbase/pgn/195801londonboys-viewer.html