Capital gains tax

Yes, exemption is available u/s 54F.

Capital Gain will be fully EXEMPT, if Residential house/flat is purchased within a period of 1 year before, or 2 years after the date of transfer of capital asset i.e. plot of land.

A condition to be fulfilled is that - you should NOT OWN MORE THAN ONE Residential house/flat on the date of transfer/sale of plot of land. 

Any Gain arising to an individual or HUF from the sale of any Long Term Asset other than Residential Property shall be exempt in full, if the entire net sales consideration is invested in Purchase of one residential house property in India within 1 year before or 2 years after the date of transfer of such an asset or in
Construction of 1 Residential House within 3 years after the date of such transfer.

In case the whole sale consideration is not invested and only a part of the sale consideration is invested, exemption shall be allowed proportionately i.e.

Amount Exempt = Capital Gain X Amount Invested÷ Net Sale Consideration

The above exemption shall be available only when the assessee does not own more than 1 Residential House Property on the date of transfer of such asset exclusive of the one he has bought for claiming exemption under section 54F.

Yes, exemption is available u/s 54F.
 

In my specific case, as already informed I am presently owning one residential flat and one residential plot. Now I am going to retain my residential flat and sell the residential plot and invest the entire Long term capital gain in a new residential flat. After the process, in addition to my existing residential flat, I will also be having the new residential flat acquired by reinvestment of the Long term capital gain. Kindly let me know, as to whether I am entitled to exemption from Long Term Capital Gains Tax if I am holding of my existing residential flat in addition to newly acquired flat from reinvestment of the capital gain.

Yes sir, Read the language of provision "Assessee should not own more than one residential house property on the date of transfer excluding the one he has brought under section 54F".
In more simple terms an assessee can have not more than 1 RHP before investing in another RHP u/s 54F.
I think it will be clear to you now.

It means assessee can claim exemption for new (second) residential house property purchased,

while he own one residential house property simultaneously. 

Hope your query is resolved now.