Don't flag it, and don't even downvote, unless it is against Stack rules somehow!
I cannot understand why you would do such a thing! Anyone in the world is entitled to ask a question on any Stack site as long as it's in with the rules of the site.
Content on Stack is moderated and handled based on the content on Stack and what it's rules are.
This is not the contest site, we are not involved in running it, and therefore anyone using this site to gain answers about a competition elsewhere are only using this site the same as every single other user - asking a valid question! Whether cheating some other site rules or not, Stack cannot and should not manage that or care about it.
Wanting to implement an entirely new flag is effectively:
Moderate and manage competition rules from another site unrelated to Stack
Is there actually anything wrong with them asking such questions?
the OP was asking us to help fix their code on Stack Overflow
"Help fix their code" not "make some code to win the competition".
I could be wrong, having not seen the competition rules nor the question you want to flag, but surely everyone who enters the competition had to learn code somehow somewhere, so why not someone writing code now and asking someone to help with it?
Perhaps that is against the competition rules, even if so, if it is not against Stack rules you shouldn't flag or downvote based on rules from another site - it is not fair.
There are probably hundreds of students asking for homework questions, getting answers, copying and pasting it and passing it off to be marked as their own.
That would be against Uni rules, are we to moderate that too?
What about people in a job, trusted to be worthy of the tens of thousands salary they receive, but in fact half their code is from people advising and even writing code for them on Stack?
Maybe their manager would state it's not in the contract and sack them.
Are we to moderate that too?
Voting and flagging is based on Stack's site rules.
What are we, World forum/competition Police?
On codechef, we are told to not share anything from code, algorithm,
or anything related to a problem from an ongoing contest, but since
users are unable to ask their questions there, they come to Stack
Overflow and ask it there.
So that is their problem, not ours.
It might be Stack Staff's problem if they request removal, but they're not obliged to remove it.
It's not like the authorities requesting illegal activity to be removed, or piracy or copyright infringement of some kind.
The questions are legit to be here, and is just someone asking for information just like any other user.
Up till now, when I encounter questions like that, I flag them for
moderator attention explaining the reason ( I don't have enough
reputation to vote to close ).
Can you tell me, disregarding the fact you dislike cheating and want the question stopped because they are cheating, what reasons based on Stack rules should the question be flagged?
If none, then do not flag it.
Incidentally. flagging a moderator just because you do not have reputation to vote to close it not how to use the site tools.
I think overall, you are using the site vote/flag etc tools in very much the wrong way and for the wrong reasons.
There are many more flag options which would warrant some kind of speed option than moderating a 3rd party external competition just to stop people cheating, especially when they've asked a valid question within the Stack rules.
Please, downvote and flag based on merits of the content on this site, not because it might not be liked by some other site.