you will have to first check in the existing POA whether any power is granted to your father to transfer the flat by way of gift and to register such gift deed with the sub-registrar of assurances
if the above power is absent in the POA, then you will have to make another 'Special Limited POA' in which you would authorise your father to complete and comply with the registration of the gift deed on your behalf
so you can have the gift deed draft and special POA draft prepared by a lawyer
after the drafts are approved by you, the lawyer will take their prints on stamp papers
for the special POA the stamp duty is Rs. 500/-
for the gift deed, for gift of property by son to father, the stamp duty is 3% plus 1% metro cess, on the market value of the flat plus 1% registration fee alongwith registration agent's and lawyer's professional fees
initially the gift deed can be stamped for Rs. 500/-
the stamped POA and gift deed can then be couriered to you at your USA address
you will then have to sign on the documents before the Indian Consulate/Embassy in the USA
Then you will have to send the signed documents back to Mumbai by courier
your father would then get the gift deed registered and comply with the registration formalities on your behalf using your special POA
the POA can also give powers to your father to sign on applicable society share transfer forms and share certification application and to submit the same to the society for name transfer in his name
likewise a power can also be given to him to apply to all the relevant authorities like electricity supplying company, etc. to transfer the electric meter and other utility bills in your father's name
your father will have to hold the flat for atleast 3 years in order to avail the long term capital gains tax exemption benefit when he sells the flat in future