Flounder in the DE Bay in June can be hit or miss. The bite usually gets better later in the summer, with August being prime. Some years it's good in June, and other years very sparse. Just thought I'd mention this cause if you go in June you may want to be flexible with what fish you target.
Two good charter boats out of Lewes are the Grizzly and the Indian.
I agree with Togger. Grizzley is good, but exspensive. Indain is good, but by far the slowest boat I've ever been on. June is early, and more than likely going to be heading to the old grounds, and that's good hike. But both Carey, and Ted are good people, and good Captain's that will try the best they can to put you on fish. If I had to pick I would go with the Grizzley, because of the first mate Doug. He does just an awesome job no matter what you're fishing for.