As others have said, I would run hard pipe if it was me, with a UL listed flexible gas connector to your grille. Now it has been a few years since dealing with NFPA 54 National Fuel Gas Code but if memory is correct you can use it if it is protected from damage within 6ft of grade.
A bigger issue with CSST is that it must be electrically bonded to the hard gas piping and that piping will need to be bonded to the electrical system in the dwelling, meaning that the gas piping must be grounded to the same ground as the electrical system with a #6 AWG wire. If I remember correctly this bonding is not required if only hard (schedule 40) pipe is used.
