Earlier quoted context omitted.
Where did that quote come from? I know that FB took some flack for their rule change and issued a second statement on it that walked things back a bit. Is your quote from that?
Just out of curiosity (I'm a non-native speaker): Is there a difference between flak and flack? Are these regional variants, maybe a US/UK thing? Would you use either, depending on exact context (literal flak-cannon vs "taking flack" phrasal verb)?
Yes sibling comment is correct, no difference other than spelling between flak and flack. Sounds like flak is more common.
It's a common idiom (at least in the US), especially regarding anything remotely political, about having multiple people "target" a person who says something they disagree with. Especially common if person A does or says something and then a bunch of news outlets/pundits criticize them for it, it's said that they're "taking flak" for whatever they did.
An important note, the expression itself does not make a value judgment or convey any sort of "right" or "wrong" or good/evil on either party. You can "take flak" for saying stupid stuff, and you can "take flak" for speaking the truth in the empire of lies [1].
[1] A refernce to Orwell's quote: "Truth is treason in the empire of lies"