Untrue, I believe you need a certain amount of karma to be able to flag.

But it's something like 20 or 25, so really trivial to hit for any genuine user. (Although it's possible there is some weighting going on, so maybe new accounts get less flagging power or something like that)

Nope, I have 213 karma and the only thing I can do is upvote comments.

Can you flag submissions?

Yes, I can.

interesting. maybe I'm misremembering and comment flagging comes with downvotes, which I guess would make some sense.