I withdrew them to Mexc (which is not good decision - to withdraw casino funds directly to exchange wallet, as exchange can flag transaction as problematic).
If you first make a withdrawal from the Freebitcoin site or any other casino to your own address and then only to a centralized exchange, it won't change much. I mean, if a CEX really checks deposits and marks funds from casinos as undesirable, they won't limit themselves to checking only the address from which the deposit was made.
But in the case of MEXC, it seems to me that you shouldn't worry about it because this exchange sometimes adds outright scam tokens, i.e. not really bother with any kind of checks.
Well, I really do not see anything wrong in withdrawing funds from a casino directly to an exchange, and this does not matter what type or which exchange, as a matter of fact, I've withdrawn funds from different casinos and sent directly to exchanges like Binance, bybit, kucoin and several others and I've never had any issues receiving the funds.
I think we all have to understand that casinos are also legitimate businesses just same way exchanges are, so it's completely wrong for any exchange to flag deposits from casino as illegitimate, except there are other issues the exchange has with the casino where the funds is coming from and decide on their own to flag payments coming from the casino.