That is a hard question to answer. What kind of wood are you ordering on your Flow hive? If it is cedar, you can put bees in it untreated. I wouldn’t, but you can. Then you can treat with Tung Oil with the bees already in the hive.
If it is pine, you absolutely must paint or seal it before you put the bees in. If you use a water-based exterior paint, you probably want it to cure for about a week before putting bees in. If you want to use an oil-based finish (varnish etc), you will need at least a month.
Where are you ordering your bees from? You might find a local beekeeper if you join a beekeeping club, and they could give you more flexibility. Just don’t tell them you have a Flow hive. Say it is a Langstroth (which it is). Everything about the beekeeping that you will need to do is related to Langstroth hive management in your area. The only thing that is different is the harvesting, and we can help with that. The reason for my comment is that many traditional beekeepers react strongly against Flow hives, and I don’t want you to have a bad experience from the start. Flow hives are wonderful, but some people find change very difficult.
I just got a couple of really nice packages of bees from Mann Lake Ltd. You might Google them and ask if you can’t find anything locally. I think COVID-19 has messed up their deliveries, and they may have some extras