Hi,
Not entirely sure the diagnosis is correct, but I think Flash can't be configured properly on some browsers installed on Solus. I've made a recap:

VIVALDI
Facebook: OK
Soundcloud/Mixcloud: songs don't play at all
Youtube: OK
isflashinstalled.com: Yes

OPERA
Facebook: videos don't play at all
Soundcloud/Mixcloud: songs don't play at all
Youtube: most videos open in 360p at max
isflashinstalled.com: Nope

FIREFOX
Facebook: OK
Soundcloud/Mixcloud: OK
Youtube: OK
isflashinstalled.com: Yes

I am using Solus 2017.04.18.0 64-bit and Budgie 10.3.1-143.

Thank you.