Probably the best way for you to go from Flores would be to go to the Santa Elena bus station and hop the next minivan to Sayaxche. From there hop another going toward Chisec, all the way to Coban if you can. When you get out at the periphery bus station, tell the cab driver that you want to take a bus to Lanquin. Don't pay over 30Q for the cab. He will take you probably to a shuttle company or maybe a bus company. Either way, you get an ides how soon the next one is leaving and maybe get something to eat. From Lanquin to Antigua there is a tourist shuttle.
There is a closer route from Sayaxche via Raxruha that you could take by public conveyance if you make it to Rax by 8 or 10 AM at the latest, but I think you would end up at the Lanquin turnoff waiting for another ride to the village. If you are planning on staying in El Retiro, you would do well to get off there. It is a bit of a trudge from town to get back there.
At Sta Helena airport is easy to rent a jeep, or a private tour to Tikal or Yaxha (here in the picture), the price is about $40,00.