There will be flaring at first, but over time they should calm down to where they only flare a little bit..
In the short finned variety I wouldn't worry too much about split fins - and if it does happen it only takes a couple of days to fuse back together.
As long as they have plants (real or fake) and decorations in their space to hide in/around, etc they should be fine and calm down once they realize the other can't get to them. Many many many bettas live in divided tanks just fine - just keep an eye on them, make sure they can't get to one another and see how they do. Let them flare and get it out of their system - but keep an eye on other signs as some don't like sharing a tank.
Look for fins that are clamped all the time, loss of color, loss of appetite, hiding all the time.. those are the signs that will say that fish doesn't like being in a divided tank. But if they are still eating, swimming around.. then flaring isn't something to worry too much about.
Place some tall plants (real or fake) along the divider to help break up the lines of sight - but even that isn't a must do, but could help and give you a little peace of mind.