I've got no sound from Flash in Firefox running my MacBook pro through HDMI cable and I've found a similar question from '15 on the, cached, Adobe Forums
When viewing video with flash player in firefox the sound is played through HDMI altough my USB headset is set as the default sound device. All other sound is played trough the default sound device EXCEPT flash player sound.
Restarting firefox doesn't help.
Reinstalling the flash player plugin doesn't help.
To which the answer says:
Yeah, this is a lingering Firefox problem, and it's related to limitations in how we had to retrofit sandboxing to the NPAPI. The best workaround is probably to just use Chrome. I forget the exact reason why (this has been a problem for years) but the low-integrity Flash Player process doesn't have permission to call into the Windows Sound APIs necessary to set the correct output target, and I don't believe that we can broker it safely for some reason.
Mozilla has recently engaged in a collaborative effort with us to improve the overall experience with Flash in Firefox by addressing some of these long-standing architectural deficiencies. Our hope is that we'll be able to provide both a secure and efficient Flash implementation all around, but that effort is going to take at least several months before it reaches customers (and we're doing incremental stuff in the meantime).
Sorry I don't have better news on that front.
The Q&A is a good two years old, I'm hoping there has been some improvements by now.