I think I found the problem: I don't have a sound card at the moment (I physically removed it from my PC because it's broken). It never even crossed my mind that that could be the issue...
I reinstalled haxe and openfl so I could test it, and then I compiled and ran one of its sample projects to cpp. It runs fine, but it also gave me a hint in the command line:
"AL lib: (EE) ALCmmdevPlayback_open: Device init failed: 0x80070490"
I'm gonna send the Kha project's executable to a friend of mine to see if it runs on his PC. If it does, then I guess that's the problem.