You're not really supposed to just add wild ccaught fish/plants to a tank with other fish do to disease..
But quarantine and some preventatives might help with that.
Not sure if killies are compatible with bettas though, maybe someone who's had them can say xD
I have read they are..I would put them in a quarantine tank for a week or two and see. I like them cause they are small, not colorful and well free lol.
From what I've heard and read, they prefer larger tanks (20+) and colder waters, closer to 72 degrees, whereas bettas like warmth, 77-79, and 80-82 when being treated for anything.
I wouldn't suggest adding the killifish, but it's up to you.