Hello Stosh, welcome to the Flow forum.
It sounds like your hive has done exceptionally well for just the one season. In around 6 weeks, you have 2 deeps established with a super on top. That is truly amazing progress. I guess the nectar flow must be fantastic in Virginia this year!
Answering your question is complicated, I am afraid.
First, many parts of the northern hemisphere have a nectar dearth in June, commonly known as "the June Gap". Do your local beekeepers say this is happening right now? If so, they won't have anything to put in the Flow super.
Second, one frame of honey in 2 deep brood boxes is not that much. My Flow hive probably has at least 6, but they are in their second year. Your bees may still be putting honey into the brood boxes for winter stores and feeding their brood for the rest of the season. They will only put excess into the Flow super once the brood nest has sufficient.
Third, did you wax the Flow frames before putting them into the super? If you don't they take much longer to accept the plastic frames. Some people have even had to wait a whole year. Some advice on that can be found here:
Sorry I can't give you a straightforward answer, but they will work the frames if you give some encouragement with waxing, and they have a good nectar flow. My bees started waxing the Flow super in about 2 days, and storing nectar/honey after 2 weeks. However, it took just over 2 months to get a ripe frame of fully capped honey. Here is my harvest from 2 frames yesterday - about 5 quarts or 14lb!