No, you can not. With your Greek travel documents you are allowed to travel inside the European Union for a maximum time frame of three months in six months.
Generation 2.0 for Rights, Equality & Diversity has published two videos, to support refugees to find a job in Greece.
In general it is only possible to book a ticket for family reunification, if you have been notified from the Greek Asylum Service, that your claim has been processed and that it is now your turn to book and buy a ticket. The Greek Asylum Service has confirmed to the Mobile Info Team, that at the moment it is temporarily not possible to book a ticket for family reunification flights.