For damaged fins, API Stress Coat should be a good addition, it has Aloe in it which is healing, a little natural salt, I use Redmond's or Orso salt (it is mined near the Great Salt Lake area in Utah) from the health food store. At mine I can get it in a bulk bag and it is about $1.50 for a couple pounds. You can use aquarium salt too. Basically any salt that doesn't have any additives like Iodine, or anti caking agents. I don't usually use much salt but I have always used about 1/8-1/4 tsp per gallon with the Bettas, and you might try some Almond leaves, or some pesticide free local Oak leaves. The tannins are good for their skin, but it will likely turn the water golden/yellowish to brown.
I have used this salt for at least 10 years. Because it has the minerals, I think it has been additionally beneficial for the fish. You can add the salt in gradually, over the course of some every couple days until you get the full dose put in, then when you do pwc, just add back that amount per gallon , dissolve in warm water before adding to the tank water (all water treated of course). You don't want the fish to accidently eat the salt. You could add up to a tsp per gallon as well for treatment purposes without problems.
(Other kinds of treatments can be higher concentrations, not necessary for him)
My understanding is that both salt and tannins create an environment which helps prevent bacterial infection.