Capital Gain would be applicable. Such transfer is taxable as the relinquishment of an asset or rights therein.

Since you sold the right in flat, you will be eligible for exemption under Sec. 54F.

2) 

Under this section, you can avoid tax on capital gains from the sale of any assets other than house property if you reinvest the money to buy another property.

3) you can claim total tax exemption by using the money you gain from selling any asset (except a house property) to buy a house property, which needs to be bought one year before the sale or two years after the sale. For under-construction properties, the new property should be ready within three years of the asset’s sale. 

To claim full exemption the entire sale receipts have to be invested.

Since the property has not been purchased by you through a registered document this cannot be considered as a capital hence there is no question of capital gains therefore you cannot pay either the LGCT or STCG taxes. 

income-tax laws that apply to a fully constructed residential house, might not apply to the sale of an under-construction house. An under-construction property is still a capital asset for income tax purposes. However, for specific provisions, it should not be treated as land or building.

When the computation of capital gain is in question, one must identify whether the asset in question is a capital asset or not. Once this aspect is figured out, one should move to identify its nature, period of holding, exemption and tax rates.

You can make it tax free unless you deal in cash

It is better to register the sale as early as possible, preferably in this financial year itself. Then you may very well invest the surplus arising out of the sale of your flat in any capital gains scheme, after due indexation. Sale of an immovable property is evidenced only by a registered document. Capital gains incidence will arise only after that.

- Under the Income Tax Act, property is regarded as a capital asset and any gains arising from its sale is taxable as Capital Gains.

- Further, if the property is held for less than three years prior to its sale, it is termed as a short-term capital asset and any gain arising from the sale is treated as a short-term capital gain.

- Further, if the property is sold after a holding period of more than three years, it is to be treated as a long-term capital asset and a gain arising from its sale is assessed as long-term capital gains

- Further as per Section 54EC of the IT Act, any capital gains arising from the transfer of a long-term capital property/asset would be exempt if the gains are invested within a period of six months in specified investments, and these investments are three-year bonds of National Highway Authority of India (NHAI) or Rural Electrification Corporation

- Since, you are not owner of the said property , then the amount received from the purchaser will not come under these headings of capital gains , and hence you are not entitled to pay the taxes for capital gains. 

Registration of property should be done , then sell , and invest the money.

Dear Client
In India, if you want to avail of the capital gains tax exemption by investing in capital gains bonds (Section 54EC of the Income Tax Act), there are certain conditions that need to be met. While I can provide some general information, it's crucial to consult with a tax professional or a legal expert for specific advice tailored to your situation. Here are some key points to consider:

Property Registration: To be eligible for the capital gains tax exemption, the property must be registered in your name. In your case, since the property is not yet registered under your name, you may not be eligible for this exemption.

Capital Gains Bonds: You can invest the capital gains from the sale of a property in specified capital gains bonds within six months of the sale to claim the exemption. These bonds are typically issued by institutions like the National Highways Authority of India (NHAI) and the Rural Electrification Corporation (REC). The maximum amount that can be invested in these bonds is subject to a cap (e.g., Rs. 50 lakh as of my last update in September 2021). The bonds typically have a lock-in period of 5 years.

Short-Term Capital Gains: If your property was held for a period of less than two years (as in your case), the gains would typically be considered short-term capital gains. As of my last update, short-term capital gains on property are subject to taxation at your applicable income tax slab rate.

Given your specific scenario, where the property is not yet registered in your name and it's a short-term capital gains situation, you may not be eligible for the capital gains tax exemption through bonds. Instead, you will likely be subject to short-term capital gains tax.