1. Without registration of the flat your father has not become the owner thereof.
2. If the builder agrees to come forward for the registration then the process of registration can see the light of the day without any hassles.
3. If the builder does not register the property then you may file a lawsuit against him to seek court's directions to him to register the conveyance deed.
4. The registration charges of the present day will be applicable.
5. After the registration is done in your father's favour and he makes a gift deed then you will be able to sell the property. Alternatively, the builder may also register in your favour.