Is it permissible for him to accept membership in a Housing Society, which will enable him to get a flat for a cheap price?

Praise be to Allah.

So long as your friend is working for the government in law enforcement, which has some kind of authority in this case, then he does not have the right to take any reward, gift or payment for doing the job he is supposed to do and for which he takes a salary from the state, because he is doing that on the basis of trust that has been placed in him. 

Al-Bukhaari (6636) and Muslim (1832) narrated from Abu Humayd as-Saa‘idi that the Messenger of Allah (blessings and peace of Allah be upon him) appointed a worker. The worker came to him when he had finished his work and said: O Messenger of Allah, this is for you, and this was given to me as a gift. He said to him: “Why don’t you sit in the house of your father and mother and see if you are given any gifts or not?” Then the Messenger of Allah (blessings and peace of Allah be upon him) stood up in the afternoon, after the prayer, and recited the Shahaadah and praised Allah as He deserves to be praised, then he said: “To proceed: what is the matter with a worker whom we appoint, then he comes to us and says, This is yours and this was given to me as a gift. Why doesn’t he sit in the house of his father and mother and see if he is given any gifts or not? By the One in the Whose hand is the soul of Muhammad, no one among you takes anything of it (unlawfully), but he will bring it on the Day of Resurrection, carrying it on his shoulders: if it is a camel he will bring it groaning, if it is a cow he will bring it lowing, and if it is a sheep he will bring it bleating. I have indeed conveyed the message.” 

And Allah knows best.