There are minibuses from Flores to Tikal park. They're pretty frequent, like every hour. I think the cost is around 40 or 50 quetzales, about US$5 or $6 -- that's round-trip. It's maybe 35 or 40 miles from Flores to Tikal.
Getting back to the Belize border there are plenty of options -- minibuses, taxis, local buses, also the S&L Travel and Linea Dorada minibuses all the way to Belize City.