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I suspect itch.io assumes that a Flash game is stand-alone. Files intended for download likely have their names obfuscated, and they're not placed in the same folder as those meant to be embedded in the game page. You might want to treat it like a HTML game instead and upload it together with a small wrapper. It's not a nice work-around, but that should do it until out kind hosts can step in an do something about it.

Great! The .html into a zip file works well! \0/

Thank you for your help!