Like many others, I highly suggest Retrodeck instead of EmuDeck. Not only it is a flawless experience, but having it all packaged in a flatpak means it won’t scatter files around for every emulator which are then hard to clean up (like EmuDeck does, usually).
You got it a bit confused! Flatpak is not a way to store roms, but a way to deliver the software (RetroDeck) onto your device. Retrodeck, once installed, will create a “retrodeck” folder in your steam deck filesystem, which will again contain folders for roms.
All you need to do at that point is to place rom files inside already existing folders for their own systems (psx, psp, etc). Those files can be of many filetypes. For example, psx roms can be in chd, cue/bin, iso, etc
It is as straightforward as it can get!