Kuwait's Personal Status Law defines three main categories of permanent and temporary prohibitions based on family relationships. The first is blood relations (nasab): you may never marry your direct ancestors (parents, grandparents), your direct descendants (children, grandchildren), your parents' siblings and their descendants, or the first generation of descendants from your grandparents (Article 13).
The second category is marriage-based relations (musahara): a man is permanently prohibited from marrying anyone who was married to his father or grandfather, anyone who married his son or grandson, his wife's mother or grandmother, and his wife's daughters (stepdaughters) if the marriage was consummated (Article 14). These prohibitions arise automatically once the relevant marriage or consummation occurs.
The third category is breastfeeding (rada'a): Islamic law in Kuwait treats breastfeeding relations similarly to blood relations for the purpose of marriage prohibitions (Article 16). However, this only applies if the breastfeeding occurred within the first two years of the child's life and involved at least five full, certain nursing sessions (Article 17). There is also a prohibition against marrying someone else's wife or a woman currently in her waiting period (iddah) after divorce (Article 19). Expats should be aware that Kuwait applies these rules to all marriages conducted within its jurisdiction, regardless of nationality.
This is general legal information, not legal advice. For advice on your specific situation, consult a lawyer licensed in Kuwait.