Gift deed from mother to daughter

Your mother cannot gift the whole flat to you as it is your father's flat. Your mother has 1/3rd share in the flat and she can gift only her 1/3rd share to you.

She has right to gift the property to the extent of her share only in the property.  After the death of your father succession opens.  Being legal heir your brother has got equal share along with your mother and you in the share of your father.

Your brother being ClassI legal heir has 1/3 rd right in share of Father(1/3rd).

Your mother can gift  her share to you.

Your brother can also gift/relinquish/sell/transfer his share to you.

The society can update you on its rules.

As per section 8 of the Hindu Succession Act, after the death of a Hindu male, the property which was belonged to him will devolve upon his 1st class legal heirs equally. Therefore, no doubt, you, your brother and your mother all the three will get equal share on your father's property.

But, in your query you have stated that the flat is in the name of your father, Mother and your's. Thus, it is understood that  you, your mother were having  joint ownership along with your father and all of you had equal right over the same.

If it is so, after the death of your father, naturally and automatically his part will devolve upon his legal heirs i.e.on your mother, brother and you. Therefore, you and your mother are entitled only for 4/9 share each on the flat and your brother is entitled for 1/9 share alone.