Bettas are native to slow moving streams and stagnant paddy fields of SE Asia. They can tolerate water that is very low in oxygen too.
Therefore, a powerful flow really isn't going to help your Betta a lot and as you say, stress can set in.
Fin rot is a bacterial infection which will only take hold when your fishes immune system is low....eg when the fish is stressed.
Presuming there are no other fish in the tank which can nip his fins, you have to look at fin rot as an option caused by the stress of fast flowing water.
A good water change with medicated water (medicated with fin rot medicine) and a change of filter may help. Keep your fighter fed well too.....they love live food and if you have any mosquito larvae in an old water butt or something, they adore them.
Good luck