What is the ruling on the actions of a husband who sits with non-mahram women and talks to his female cousins, flirting with them under the pretext that they are like his sisters and they grew up together?

The husband's aforementioned actions are objectionable. Family gatherings where Sharia-compliant regulations are not observed are impermissible. His female cousins are non-mahram to him, and he is not permitted to speak with them except out of necessity. His statement that they are like his sisters holds no weight. The wife's anger towards her husband because of these actions is justified, and jealousy in such a situation is praiseworthy.

The advice for the wife is to be patient with her husband and advise him kindly, seeking assistance from those who hold influence with him, along with supplicating for his guidance.