Maybe partially, but to them, the cooler is their hive. They will not leave it if there is brood on the comb that they made in the cooler. If you want them in your Flow hive, you might do better to get an experienced beekeeper to help you do a cutout. That way, you get the comb from the cooler into your hive frames, and hold it in place with rubber bands. You then put the frames into your new hive, and most of the bees will now rehouse in your Flow hive. The bees attach the comb to the frames and chew off the rubber bands. It isn’t easy to do if you have never done it before, so I really suggest asking for some help.
You will need to remove the cooler though, because to the bees it now smells like home, and they will keep going back to it.