Hello, normally you can break the item frames, but you don't break it inside of PS block.
And I don't any flag to block this

Also suggestion, to create any method to flags to not be changed of value, for example I would some flags be always activated and the user can't change her status. And if is possible to add only the Owner can change the flags, because sometimes you add a other user to it and it can change the flags and later other user can grief all.

I'm using the latest build of PS for Spigot 1.8.8