Okay, so I've been a DM for a few years now. Where I'm from we have a decently sized DnD club. I run for said club, and we are not allowed to kick players from the club. The issue is that one of the players (who has previously been a problem player) has developed a crush on another player OOC, and he is now flirting with said player IC and it's making things awkward. Without kicking him how do I deal with this? Also, he's been cheating, any help on how to deal with that is also appreciated, but is a secondary objective.

Who is in charge of the club in general? I would forward the matter to that person or persons if you are not comfortable confronting this issue. However, this is one of those matters where you may want to step in after the game and be pretty blunt about how he is being inappropriate, especially if he is making the other player uncomfortable. 

As for the cheating, maybe also make a point after the game to call him out on it. There's really no good way to magically stop people who cheat from cheating short of calling attention to the behavior. You can mitigate the problem in-game by self-correcting things on your side of the screen, but that won't actually solve the problem and in-game punishments are never really seen for what they are and are highly discouraged anyway. 

Is it making things awkward for the other person, or awkward for you or other people? If the subject of this guy's attentions are making their target uncomfortable, then that sounds like harassment (or the beginnings of it) to me. If a club isn't willing to enforce a "no-harassment" policy, despite the "no-kick" policy (which I think is stupid), then I would get out of there quick while also alerting whoever runs it as well as the owner of the establishment (if they're not the same person).

As for the cheating, I can't offer much without knowing how, exactly, they might be cheating. There are tips and tricks a DM can use depending on the cheating methods employed.

I agree that you probably shouldn't call the play out on it during play. At least not before making a general, table/group wide rule about whatever it might be.
i.e. rolling out in the open, no snatching it up right after, allowing confirmation of the roll, etc. Only allow in-character conversations at the table - anything said at the table is considered in-character, and you can rule on the spot when what they said wouldn't be permissible. Make sure you review and have a general understanding of their characters and character sheets.

We could probably come up with other such tips and tricks if we knew how the player was actually cheating.

Thanks for the advice. I probably will forward the matter and see what kind of response I get. I've confronted the cheating issue last year. Said player usually denies.

 Well there are ways to mitigate some cheating if we know what sort is being employed.

Awkward for the other person. The club is generally good at enforcing its rules. However, the issue was only brought to me a few days ago, and I thought getting the advice of other DM's would be good. As for the cheating, it is him rolling and then declaring a high roll no matter what he rolled. I'm probably going to institute a roll out in the open rule, but I was wondering if anyone had other ideas to help curtail the cheating.

What? You play at a table, face to face, and your players hide their dice rolls?  What for?

The problem is he rolls then scoops up the dice before anyone can see what he rolled and declares a high roll. It's a common occurrence among cheaters.

If your other player is feeling uncomfortable, it'd mean a lot (a super lot) if you stepped in and took the hit for them. Since there is a no kick rule in your club they are already taking a vulnerable step by joining in... Showing that you're willing to go to bat for them by first asking the player to stop, and then demanding it if asking does not go well, mean so much to keeping a safe feeling not only inclusive, but safe.

Source: a player who's had this shiz happen and not gotten the support, and felt a tonne of anxiety over whether to keep playing vs whether it's worth it to even try to go if the offender is always getting a free pass. It sucks when more vulnerable players get edged out because one person has crappy behaviour.

That's an easy problem to fix.

DM Rule:  The roll stays on the table until the situation is resolved.  Done.

I've discussed the situation with the player, and she said that she'd see if it continued this session and if it did she'd tell him to stop. I'll, of course, be there to back her up, and will inform the head organizer so that worst case if it doesn't stop we can move the offending player to a different table. 

What is the typical age/demographic of your Players?

I would argue that if your Players are all legal adults, that maybe mitigating the flirting situation isn't your responsibility.

That doesn't mean you can't intervene to some extent - have a word with the flirting Player " Hey X, your behavior is really making Y uncomfortable - maybe tone it down, of we're going to lose Y as as Player, OK?" - but that's being a good friend/protector/social facilitator - not part of the role of the DM.

If you're dealing with legal minors ... then the situation gets very sticky.

As for cheating - roll on the table, in the open, or it doesn't count. If the DM doesn't see it, it doesn't count.

I am dealing with minors.

Report the crush issue to the club organizer, the way you did.  Especially with minors, things can get sticky otherwise.

As for the dice, you're the DM.  You're well within your rights to say that any roll you didn't see is a roll that doesn't count.  That's not even a DM house rule, that's pretty much how the game runs.  If the player rolls, scoops, then declares his roll, he gets to reroll.  if he does it again within that session after being told to leave his dice where they land, he rolls again with disadvantage.  He does it a third time after that, whatever roll he's trying to make he gets to automatically fail, and same with every other chance after that.  Make sure that what he's trying to accomplish with this shenanery - succeeding on his checks - is the opposite of what he gets for doing it.

Part of the DM job is enforcing the rules.  If this bozo is playing reindeer games with his dice, then either he learns to stop doing that or you start rolling for him/ask another player to roll before asking Bozo for his modifier.  if he yowls and complains, you can inform him that this is simply good gaming etiquette and only folks who're breaking it have any cause for complaint.

Well, we had another session and he seems to have stopped his that guy behaviors. I saw most of his dice rolls this time, and he mostly stopped the flirting. 

What a pleasant resolution lol
I've been reading this thread for the drama (the juicy title hooked me) to kill time at work and now I feel invested in the plot haaha
Glad to see it worked out! (for now?)

Hopefully, this nips it in the bud now.