Is Salatul Tasbih Legislated?
Question

Brother, I wanted to know the status and ruling on "Salat-al-Tasbih" as reference is given to it  from Abu’Dawood and Tirimdhi, but without the hadeeth (narration) number and it says, "Our Beloved Prophet Muhammed (peace and blessings of Allah be upon him) said to his uncle (father’s brother) Sayyiduna ‘Abbas (may Allah be pleased with him), Oh uncle shall I not give you, shall I not grant you, shall I not award you, shall I not do mercy on you; when you do 10 things Allah will forgive your sins, of the future and of the past, new and old, those you have forgotten and those you did knowingly, big and small, hidden and revealed. Then he (peace and blessing of Allah be upon him) taught him the way to pray Salat al-Tasbih and then said if you can pray this salah once a day, if you cannot pray once a day then every Friday, and even if this is not possible then once a month, and even if this is not possible then once a year, and even if this is not possible then at least once in a lifetime (Abu Dawud and Tirimdhi) and it said that this phrase “Subhan Allahi Wal Hamdulillahi Wa La ilaha illal Lahu Wallahu Akbar " should be recited in different steps in Salah to make it to a count of 300. What is the ruling on this and is this from an authentic source?
Praise be to Allah.Hadith about Salat al-Tasbih
Abdullah Ibn ‘Abbas narrated: The Messenger of Allah (peace and blessings of Allah be upon him) said to al-’Abbas ibn ‘Abdul-Muttalib: ‘Abbas, my uncle, shall I not give you, shall I not present to you, shall I not donate to you, shall I not produce for you ten things? If you act upon them, Allah will forgive you your sins, first and last, old and new, involuntary and voluntary, small and great, secret and open.
These are the ten things: you should pray four rak'ahs, reciting in each one Fatihat al-Kitab and a surah. When you finish the recitation of the first rak'ah you should say fifteen times while standing: "Glory be to Allah", "Praise be to Allah", "There is no god but Allah", "Allah is most great". Then you should bow and say it ten times while bowing. Then you should raise your head after bowing and say it ten times. Then you should kneel down in prostration and say it ten times while prostrating yourself. Then you should raise your head after prostration and say it ten times. Then you should prostrate yourself and say it ten times. Then you should raise your head after prostrating and say it ten times in every rak'ah. You should do that in four rak'ahs.
If you can observe it once daily, do so; if not, then once weekly; if not, then once a month; if not, then once a year; if not, then once in your lifetime.” (Abu Dawud, 1297)
Is Salat al-Tasbih legislated? 
The scholars (may Allah have mercy on them) differed as to whether Salat al-Tasbih is prescribed in Islam. The reason for this difference of opinion concerning it is the difference of opinion concerning the soundness of the hadith which speaks of it. The prominent scholars are of the view that it is da‘if (weak). 

Ibn Qudamah (may Allah have mercy on him) said in al-Mughni (1/438): 

“With regard to Salat al-Tasbih, Ahmad said: I do not like it. It was said to him: Why? He said: There is nothing sahih (authentic) about it, and he waved his hand as if dismissing it.” 

Al-Nawawi (may Allah have mercy on him) said in al-Majmu‘ Sharh al-Muhadhdhab (3/547-548): 

“Al-Qadi Husayn, and the authors of al-Tahdhib and al-Tatimmah said: Salat al-Tasbih is mustahabb (desirable), because of the hadith narrated concerning it. But this view of it as mustahabb is subject to further discussion, because the hadith in question is da‘if (weak), and it involves changing the regular format of the prayer, so it should not be done without a hadith (to support it). Al-Tirmidhi said: More than one hadith was narrated from the Prophet (peace and blessings of Allah be upon him) concerning Salat al-Tasbih, but not many of them are sahih. And al-‘Aqili said: There is no proven hadith about Salat al-Tasbih.”

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said in Majmu‘ al-Fatawa (11/579):  

“The best of the reports narrated about these prayers is the hadith about Salat al-Tasbih, which was narrated by Abu Dawud and al-Tirmidhi, but nevertheless none of the four imams spoke of it; in fact, Ahmad regarded the hadith as da‘if, and these prayers are not mustahabb.” 

Al-Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said in Majmu‘ Fatawa Ibn ‘Uthaymin (14/327):  

What seems more likely to be correct in my opinion is that Salat al-Tasbih is not sunnah (from the prophetic teachings), and that the hadith about it is da‘if. This is for several reasons: 

The basic principle concerning acts of worship is that they are disallowed unless there is proven evidence that they are prescribed.
The hadith is mudtarib (weak); there is a difference of opinion concerning it for several reasons.
None of the imams regarded it as mustahabb.
If this prayer was prescribed, the ummah would have narrated a report concerning which there was no doubt and it would have been well known among them because of its great benefit. 

Moreover, it is not like any other act of worship, because there is no act of worship in which so much choice is given that it may be done once every day, or once in a week, or once in a month, or once in a year, or once in a lifetime. Because the weak hadith states that it is of great benefit and because it is not like any other act of worship, yet it is not well known and was not transmitted, we know that there is no basis for it, because if an act of worship is different from other acts of worship, and if it were of great benefit, people would pay attention to it and transmit it, and it would be popular and well known. Because that is not the case with regard to this prayer, we know that it is not prescribed. Hence none of the imams regarded it as mustahabb, as Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said. Among the nafl (voluntary) acts which are proven to be prescribed in Islam there is a great deal of goodness and barakah (blessing) for the one who wants more, so he should be content with that which is proven, and he has no need of that which is the subject of differences of opinion and doubts.”
For more information, please see the answer to question no. 14320
And Allah knows best.