I recall reading a hadith somewhere probably in Sunan nasai, that umm salama reported that, the prophet (sa) said that, reciting subhanallah, alhamdulillah and Allah Akbar ten times each in salat after tashahud will result in Dua being accepted made after them. How authentic is it? Can anyone provide the main source I mean reference?
Sunan an-Nasa'i 1299 appears to be the specific hadith you're looking for:
It was narrated that Anas bin Malik said:
"Umm Sulaim came to the Prophet (ﷺ) and said: 'O Messenger of Allah (ﷺ), teach me some words that I may supplicate with during my prayer.' He said: 'Glorify Allah (by saying SubhanAllah) ten times, and praise Him (by saying Alhamdulilah) ten times, and magnify Him (by saying Allahu Akbar) ten times, then ask Him for what you need; He will say: 'Yes, yes.'
Grade : Sahih (Darussalam)
It's listed as sahih (authentic).
There seems to be a range of ahadith which overlap with this one:
...When he stood up, be uttered the takbir (Allah is most great) ten times, and uttered "Praise be to Allah" ten times, and uttered "Glory be to Allah " ten times, and uttered "There is no god but Allah" ten times, and sought forgiveness ten times... -- Sunan Abi Dawud 766 [Hasan Sahih] (sunnah.com)
...He said, "Shall I not tell you a thing, by doing which, you will catch up with those who are ahead of you and supersede those who will come after you; and nobody will be able to do such a good deed as you do except the one who does the same (deed as you do). That deed is to recite 'Subhan Allah ten times, and 'Al-Hamduli l-lah ten times, and 'AllahuAkbar' ten times after every prayer." -- Sahih al-Bukhari 6329 (sunnah.com)
Umm Sulaim came upon the Prophet and said: "Teach me some words that I can say in my Salat." So he said: "Mention Allah's Greatness (saying: Allahu Akbar) ten times, mention Allah's Glory (saying: Subhan Allah) ten times, and mention Allah's praise (saying: Al-Hamdulilah) ten times. Then ask as you like, (for which) He says: 'Yes. Yes.'" -- Jami` at-Tirmidhi 481 [Sahih] (sunnah.com)
All in all, this looks like a reliable hadith.