I live just outside Brisbane, Australia, and have had a Flow hive since September last year.
I added the Flow Super to the brood box (which was about 70% full) just before Christmas - I know this was maybe a bit early, but I was going away.
An inspection at the end of January showed that the brood box was getting fuller (maybe 90%) but the Flow hive was not being used, except maybe for a bit of filling the gaps between cells.
Another inspection last weekend showed the brood box completely full, with lots of larvae and at least 10 queen cells “growing”, but the Flow Super still completely empty.
I’m concerned that the bees have decided not to use the Flow Super, and are planning to swarm due to lack of space.
You need to do some preventative swarm management prior to those queen cells hatching. Basically taking either the queen cells and some bees or the existing queen and some bees into another box (nuc or full sized super). This is assuming they are swarm cells and not supercedure cells.
Also you can encourage them up into the flow super by waxing the flow frames, rubbing burr come on them and/or spraying with sugar water. @Dawn_SD has a great cut and paste she provides to answer this question and there is a good FAQ on the flow website. It is also predicated on having a nectar flow.
But first things first do the swarm management before they swarm and you loose half your bees.
I have a friend with a nuc box, so will try to split the hive as you suggest.
I tried rubbing the flow frames with burr comb a while ago, and over the weekend I used some honey from the brood box to smear over the flow frames - hopefully they’ll get the idea soon.
We’re getting a lot of rain here at the moment, so finding a suitable time to open the hive is not so easy.
Bees finding nectar in rain is not very likely either, so you made just need to be patient on the super. However, Adam’s swarm prevention advice is absolutely spot on.
If last weekend showed 10 growing swarm cells it’s almost too late: Once they are capped it’s usually "bye bye time for the queen and her entourage.