Depends on nectar availability and if what is coming in to the hive is outpacing what is being used by the hive.
I have the same set up as you, 2 brood boxes with the flow super on top. I put my flow super on about 2 weeks ago and the bees started to seal the splits at the top and bottoms of the cells but no nectar. The top brood box was loaded with nectar and brood in various stages when the flow went on but the bottom box was only about 70% utilised. I just looked at them again today and there is some nectar in the flow super now (only a small patch of cells on one of the middle frames) but the top brood box now has full capped honey and the bottom brood box basically the same). The lesson… I thought the hive was “full” (or close to it) but it was two weeks short of that now I realise.
I probably slowed them down slightly by introducing the flow super too early but they are picking up the slack now.
In short - once they run out of room elsewhere in the hive, they will go up to the flow frames.
And yes they mostly seem to work the centre frames first so you’ll need to pull them every now and then to check the progress imo.