Another downside of flatpak is that I don't trust upstream devs to have my best interests at heart, but I trust Debian developers far more. I've seen upstream do some annoying or stupid shit and the Debian maintainers not budging.
I think it was poppler or evince that decided they were going to enforce the no-copy-and-paste bit you can set on pdfs. Debian patched it out. I've seen Mozilla decide they were going to enforce their trademarks. They carved out special exceptions for various distros but that still would have meant you would have to rename Firefox if you were to fork Debian. Debian had none of it. There were many dodgy copyright and licensing problems upstream devs gave no shit about. Debian not including these often eventually put pressure on them to fix this shit or for some replacement to get developed.
Anti cheat software tries to find cheats running on the computer, and in order to that, so called kernel-level anticheat hooks into NT (Windows kernel) internals, and runs at the highest possible privilege level. It has to do that so it can monitor everything going on in the system. If it didn't do that, the cheat could just hide from the anticheat software by running with superior privileges.
Wine does not implement undocumented/internal parts of NT, and neither does it run at an elevated privilege level. It also cannot realistically implement any and all possible NT kernel internals, and it cannot possibly hide the fact that it's actually wine, and not real Windows, from any program that really wants to figure this out.
If wine tried to implement a specific workaround for a specific anti-cheat software/version, in order to it trick into thinking it's running on a real Windows system with elevated privileges, the anti-cheat vendor would likely interpret this as a kind of deception, and they could easily update their software to detect this situation.
Theoretically, anti-cheat vendors could do kernel-level anticheat for the Linux kernel specifically if the game runs on Linux, but this has problems: First of all a general backlash and complete lack of cooperation from the Linux community (btw, Microsoft isn't too happy about them doing this on Windows either, and they might at some point do something about this, since it's bad for security and stability). Also, Linux kernel internals aren't at all stable, and so just practically you cannot hook into the Linux kernel nearly as easily as you can into NT.
Some anti-cheat vendors do support Linux though, but only optionally if the game dev allows that. In practice, this just means many checks will just be disabled on Linux, which is presumably why many games do not enable the Linux support.
tl;dr: No. Only the anti-cheat vendor / game dev can realistically fix the situation, and they may not want to because it'll be worse at actually detecting cheats on Linux in practice.