Once the Gift Deed is registered and if the flat in question was acquired by your father from his self earned, income, then your sibblings would not be entitled to claim any share in the property.
If you have gifted the property to avoid payment of any government dues including income tax and/or to avoid repaying of any dues owed by you to third parties, then the Gift Deed can be defeated on the grounds of Fraud and the property or your share in the property can be attached, despite the execution of the gift deed.
Yes, post the gift, society needs to be informed of the same with proof to effect transfer from one owner to the other and apply to the Society with the necessary transfer forms for transfer of flat.