What happens in terms of reincarnation if an evil person dies with a clear conscience?

Nothing.

We haven't even objectively observed souls, spirits or any post-death intelligent sentience, let alone reincarnation, and let alone to a point we can catgeorically state that it happens to know what happens to evil people.

When an evil person does, the best outcome would be that their evil deeds are exposed, restitution is made to the victim/s and the rest of society learns from the mistakes made that enabled the evil in the first place.