I am using both of them without any problem.
The main advantage of Flatpaks (and things like AppImage) is that you have a single “executable” with everything you need and sometime that is useful even if the software is Opensource but the building dependencies are a nightmare. Subsurface (a dive log software) is an example.
If the AUR package is a simple build (or a binary which is a converted package) then go for it. If you need to start building a lot of additional package from AUR to meet the dependencie then I would suggest, in order, to look for the Flatpak (or AppImage) package or to install an helper to build the packages
Only real option is to crypt them before putting them on the VPS, but at this point a VPS is pretty useless.