If you have received this kind of warning message from an exchange platform, then you can feel free to send money from your own wallet to the gambling platform. I have deposited money from the exchange platform to the gambling platform, in that case, I did not receive this kind of warning message from the exchange platform. Maybe they sent you a warning message for your safety, but I think you will not have any problems, you can deposit money from the exchange itself. Also, if you have any problems, you can talk to the exchange platform team directly and get everything cleared up.
I think very differently than you.
If I receive such messages, I'd like to withdraw my money in an account on that exchange to either my non-custodial wallets first, before broadcasting it to my gambling accounts.
It is risky and kind of suspicious if I withdraw all my fund from that exchange to a gambling account that was already flagged by the exchange system. Withdraw it to one or some non-custodial wallets is a safer choice. It's my keys, it's my coins; and the exchange did not flag those addresses in my non-custodial wallets.
Or I can create completely new non-custodial wallets as destinations of my withdrawal.
After receiving red flag, and continuing to store your fund on the exchange, or continuing to withdraw it to a gambling account, is too risky, that I would avoid as most as possible.