For a healthy Betta, fins should heal no matter what. Really bad damage (or even an old betta) will leave wonky looking fins, meaning they won't grow back to what they used to be.
One case, was a rescue. He was tossed in with cichlids or something stupid. NO fins left. Took him in, healed him up... Scales grew back, and fins began to grow back slowly.
Shiloh had more difficulties growing his fins back, also due to the immense amount of fin loss (his faceplate was also torn, and his beard too!) but for his condition he did pretty dang good.
THOSE are major damage fish. For simple damages... Fin rot, blown fin (over flaring usually), ornament-related tears, fighting tears... They can heal pretty well, pretty fast. Time frame: 2 days to 2 weeks.
Also depends on the husbandry. If it might be fin rot... Up the water changes. If the fins are ripped, keep up on your water changes, to avoid infections. Septicemia, is caused from yucky water... The bacteria gets into wounds, like bitten or torn fins, and is just a right out pain.