What happens to children of incest?

No single answer: Effects of incest vary widely and depend on many factors--age of child, gender of child and of abuser, level of coercion (psychological or physical force) involved, extent and duration of abuse, reaction of others if they learn of abuse, etc. One fairly clear finding is that those who were abused are both more likely to be abusers and to be unable to protect their chidlren from abuse.

If you mean children: from the union of 2 people who share at least 1 common ancestor, the closer the relation, the higher the risk of their fetus' inheriting harmful genetic mutations from both parents & having an autosomal recessive disorder, a weakened immune system &/or early demise from the percentage of shared genes. OB's & fetal-maternal specialists work with prenatal genetic counselors to assess risk.