Hello Kouvueshouch92
Completing the correct answer from @Thibcabe, the official routing is Geneva-Airport - Visp - Zermatt.
See schedules here: www.sbb.ch/en; simply enter the start and end destination as from/to destinations and the trip planner will get you the fastest connection.
A detour via Brig is not necessary and would only be required if you were taking the Eurorcity (EC) train. However, the IR trains are less busy and offer sufficient number of seats. A reservation is therefore neither required nor possible.
Regarding your Swiss Travel Pass Flex: you must have it activated before boarding a public transport vehicle. Also, it requires your physical passport or national / state ID card upon ticket check. For activation, see this page: https://www.activateyourpass.com. Once activated, it offers free travel at will on the day of validity.
Kind regards,
Roland