The Mac computer platform has no problem at all playing Flash movies.
It's only the Apple mobile devices that don't support Flash, so iPhone, iPod Touch, and iPad won't see the Flash movie unless the user has installed some app which allows Flash to play on that device.
But if you do what YouTube does, and encode the video as H.264, then it'll play with no problem on those mobile devices, just like there's no problem playing YouTube videos on them.
In case you need it...
How to encode H.264 video
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