Your question is not Arch specific, it's "should I use flatpaks?" And the answer in my opinion is probably no.

Flatpaks are a good idea to isolate certain applications and to provide a uniform way of installing packages. So there might be some apps that are not available in your native package manager, but do provide flatpaks. For those cases flatpaks are probably preferred. But Arch based distros have the AUR, so there are a lot of apps that aren't packaged for Arch that you can still get as a native package. Sure, using the AUR is risky and if you're not on actual Arch things might break sporadically because of mismatched dependencies (although I think CachyOS is full parity of packages with Arch, so that's maybe more of a Manjaro warning).

But flatpaks are clunky, bloated, require annoying permissions to be set to do basic things, and require you to update two package managers to do a full system update. They are more appealing for systems where you don't want to give users root access but still allow them to install programs, but for your own computer I have never seen the appeal.