Can I gift my property to my two sons to avoid capital gains taxes?

Ans: An undivided property that has been passed down from father to son for at least four generations is referred to as an ancestral property in India. In case of ancestral property, you do not have a right to deny any one or more of your legal heirs of their share. In your case, as written by you, it is only an inherited property passed down to you from your father. You thus have the absolute right to Will or gift it the way you wish to.

Ans: Yes

In case of gift, period of holding of previous owner will be added

Ans: 01. In absence of information, I suppose the property being sold is a Long Term Capital asset.
02. Please work out Cost of ancestral property, so that you can work out Capital Gain on it, after reducing the same from sale amount of Rs.29.00 lakhs.
03. LTCG will be taxed @12.50% with Indexation or @20.00% with Indexation. You can choose the option, where the LTCG is less.
04. Your father can Gift the amount to both sons without any tax implications. The Gift should be by cheque or online transfer and not in cash. Better if proper document for gift is prepared.
05. Both sons may use the gifted money in the way they like, including re-payment of loans, either housing or other loan.
Most welcome for any further clarifications. Thanks.