You can. I don't know if itch.io can embed it though. Also, no browsers come with Flash by default these days so even if it was embedded it'd require 3rd party extensions. And it's not common for people to run Flash locally, however there's likely a way for you to create executables that don't require other software. Something to look into.
I remember there's a build option can build an executable file for windows(*.exe) instead of flash player document(.swf). I did it with Flash MX 2004 several years ago.
