The flow hive supper is on top but the bees keep filling in the lower area and the queen is loosing space to lay eggs. We believe she just swarmed and we missed it because there are no eggs and she is gone. Any suggestions on how to get them to move the honey while we order a new queen?
If you can get a frame of brood from another beekeeper, you could put that into the brood box. If they are queenless, they can use the eggs or very young larvae to make another queen. If you have queen cells in the brood box, you don’t need to buy a queen. The hive will make their own. In fact, they usually do that before they swarm. The old queen leaves with the swarm, and the new queen takes about 4-5 weeks to emerge, mate and start laying. If you are very unlucky, she may get lost on her mating flight, but that usually doesn’t happen. However, you may well be in a region of Africanized bees, in which case you will need to buy a mated queen, and destroy any queen that the hive has raised on its own. I would ask your local bee club.
For the honey bound brood box, I would take one or two of the full frames of honey out of the brood box, and put an empty frame (or 2) of foundation somewhere near the middle of the brood box, alternating them with drawn comb. They will then draw out the comb on the new frames, giving the queen space to lay. Putting the new frames near the middle of the box makes them more attractive to use as brood frames, rather than for honey.
The frames of honey can then either be stored in the freezer, extracted, or you could even put them in the Flow super instead of one or two Flow frames. The smell of honey and wax in the Flow super might help the bees to get the idea of putting honey up there too. Don’t leave them in for long though (a couple of weeks at most), or you will get crazy comb, because they don’t have the same dimensions as Flow frames, and that messes up the bee space between the frames. The important thing to know is whether you still have good nectar flow at this time of year. In subtropical Florida, you may, but your local bee club would be the best source of information about this. 
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