The "gamification" is mainly built around reputation, so it is straight forward to get a ranking of community members by reputation points (example: Stack Overflow).
I did a bit of searching, but I found no simple way to create such rankings for other numbers, such as "helpful flags", "posts edited", or "vote count". So: how to get to such rankings?
(I am almost certain that my question must be a duplicate, but again: I couldn't identify one.)
Ranking by votes and edits are already there, one click away: (Voters and Editors tabs)
e.g. All Time top voter of Stack Overflow is gnat with no less than 104,149 votes cast. (!)
As for helpful flags ranking, it is already asked for in Is there any place to see a leaderboard of top "Helpful Flaggers"?.
For helpful flags, you can check which users have the Marshal badge; if there are not too many, you can examine their profiles and fetch the actual number of helpful flags. I know someone who did this for Ask Ubuntu, and without realizing I wrote this very answer I have written a script for this as well which I shared here.
Up- & downvotes are rather easy, they are stored on the user record in SEDE. Example query here. Total votes is even easier, see @ShadowWizard's answer.
