How to Get to Flores
From Guatemala City
Also see Guatemalan Bus Schedules
The simplest and most expensive way to get to Flores is to fly. Grupo TACA has both an afternoon and a morning flight to Flores. TAG has a morning flight. There is not a lot of competition, so don't any expect good prices.
Autobuses del Norte runs a first class "plus" bus between Guate and Flores day and night and is probably the better deal in price versus quality than Linea Dorada. Linea Dorada's website is Tikal Mayan World, and it runs "luxury" older buses to and from Flores. If you can sleep on a night bus, going at night would be the better approach, because the route via Rio Dulce and Poptun is not very scenic.
Fuente del Norte also runs buses that way and there are credible reports of it having first class service. Reportedly, inside the first class buses there are also 12 deluxe seats, which might very well be better for sleeping. This is the one I want to try next time.
I came in once on a less than first class overnight bus, planning to quickly head onward to Tikal, but there were no shuttles waiting, only cabs. Because of that, we got a cab to the San Juan agency and waited for one of the hourly on the hour shuttles.
Whether you arrive by airplane or first class bus, there will be both van drivers and cabbies offering rides to Tikal or Flores. A very short walk to the highway can get you a cheap ride in a tuk tuk into town. Flores is just a short distance, so don't figure on paying a lot. Until the tuk tuks came, I had begun to walk it.
Also whether flying or busing in, an option I like for returning to Guate is to hop a van from the bus station to Sayaxché, another to Cobán and an actual bus back from there. This opens up other options for your return, such scenic views and visiting places along the way, such as the Cancuén ruins or the (to me) highly overrated Semuc Champey.
To Flores From Cancun
If you have more time than money, you could get relatively cheaper flights into Cancun and schlep through Belize. Realize that each time you leave Belize will cost you $18.75 USD for the privilege, so it isn't cheap. A really good approach is to try to make it to Chetumal for the night. It's a pleasant town to spend a night in and the express buses to Flores leave from its station early in the morning.
From the Cancun airport, you have the option of taking a bus straight to Playa del Carmen and either changing bus stations to continue in first class to Chetumal or to take one of the much slower second class buses onward. That bus now also goes to the ADO station in Playa for onward travel to Chetumal in first class buses. You can also backtrack into downtown Cancun and hop a bus straight to Chetumal.
If your plans also include visiting the Highlands of Guatemala, I would suggest that you look more seriously into flying into Guate.
Once you get into Chetumal, Belize Bus Blog is the website with the information about moving onward.
Good luck!