Occasionally, when I flag during another player's turn, my ranking may change between the moment I click the flag button and the moment the server processes the click. While I may click on the flag when it says 3rd, the server will see me as 4th and accept the flag for that position.

Of course, the easiest way to work around this is to only flag in your own turn, but sometimes you just need to flag at another time. Circumstances changing, etc.

I assume the client sends some "FLAG" signal to the server when you check the box. The problem would be solved if it sent the position currently displayed along with that signal. Something like "FLAG 3". When the server receives a FLAG signal, it simply checks whether you are still in that position before considering you flagged.