Welcome to the community @marchellodev!
Strictly confined Snaps can access users’ files with the home and the removable-media interfaces. home is auto-connected by default and you can request auto-connection for removable-media.
Another possibility is to use XDG Desktop Portals, but I’m not sure if Flutter supports that. @kenvandine, do you know if Flutter supports portals?
PS: To avoid confusion: I’m not an official reviewer, just a community member.