I do not see the phi(1020) meson appearing in the list of transportable Fluka particles. Does it mean that this particle (resonance) is discarded completely?
No: FLUKA distinguishes between particles that are produced (COMMON block PART) and particles that are transported (COMMON block PAPROP). All particles and resonances listed in Particle Data Group, with the exception of those containing quarks heavier than charm, are produced. Those which have a very short lifetime, i.e. the resonances with hadronic decay, are decayed immediately after their production. The reason is that even at the highest energies their path would be irrelevantly short. In particular phi(1020) is indeed produced and has its decay list according to measured branching ratios, in this case K+K- (49.2%) and Klong Kshort (34%).
Internally to the code, produced particles and transported particles have different numbering schemes. Only transported particle numbers are normally accessible to the user.