Praise be to Allah.

Firstly: 

“Du‘aa’ Kumayl” is a very well-known supplication among the Shi‘ah, who are very keen to recite it every week on the night of Friday, and on the night of the fifteenth of the month of Sha‘baan (Laylat an-Nusf min Sha‘baan), in accordance with reports that speak of its virtue and far-reaching effect in self-discipline, and because of what it contains of sublime meanings – or so they claim. 

Muhammad Baaqir al-Majlisi said concerning this du‘aa’: “It is the best of du‘aa’s and is the du‘aa’ of al-Khadr (peace be upon him). It was taught by Ameer al-Mu’mineen (peace be upon him) to Kumayl, who was one of his closest companions.” 

Al-Qummi said: “It is one of the well-known supplications, and is to be recited on the night of the fifteenth of Sha‘baan and the night of Friday; it suffices against the evil of one’s enemies and it opens the door to provision and forgiveness of sins.” 

See the following link:

http://www.islam4u.com/almojib.php?rid-636 

In the report of this du‘aa’ it says that ‘Ali ibn Abi Taalib said to Kumayl ibn Ziyaad: “Sit down, O Kumayl. If you memorise this du‘aa’ and recite it every week on the night of Friday, or once in a month, or once in a year, or once in your life, you will be sufficed and supported and granted provision, and you will never be without forgiveness.

“O Kumayl, because you have accompanied us for so long, we should give you what you ask for.” 

Then he said: “O Allah, I ask You by virtue of Your mercy which encompasses all things, and by virtue of Your power by which You dominate all things and everything submits to it, and by virtue of Your might by which You overcome all things, and by virtue of Your power, which nothing can resist, and by virtue of Your greatness, which encompasses all things, and by virtue of Your sovereignty, which transcends all things, and by virtue of Your eternal Countenance which will remain after all things cease to be, and by virtue of Your names which filled the space of all things, and by virtue of Your knowledge which encompasses all things, and by virtue of the light of Your Countenance which illuminates all things; O Light, O Most Holy, O First of the first, O Last of the last, O Allah, forgive me my sins which weaken all bonds. O Allah, forgive me my sins which bring down divine wrath. O Allah, forgive me my sins that remove blessings. O Allah, forgive me my sins which detain supplication (and prevent it from reaching You). O Allah, forgive me my sins which bring down calamity. O Allah, forgive me all the sins I have committed and every error I have made… “

This is a du‘aa’ with an over-wrought poetic rhythm to it which does not sound like the words of any Sahaabi, and it is far removed from the light of Prophethood. 

This du‘aa’ does not have any known chain of transmission from ‘Ali (may Allah be pleased with him) according to Ahl as-Sunnah. Rather it is well-known among those who believe that telling lies against Allah, His Messenger and His close friends is an act of religious devotion and a means of drawing closer to Allah. 

Secondly: 

Even if we assume that all of its words and meanings are good, it is not appropriate to call upon Allah with this du‘aa’ and recite it regularly, because in addition to it being a fabricated du‘aa’ that cannot be soundly attributed to Ameer al-Mu’mineen ‘Ali (may Allah be pleased with him), it has also become a slogan or symbol of the Raafidis and others of their ilk who follow innovation. It is stated above that they regard it as holy, venerate it and hold it in high esteem. Something that is like that should not be taken as a religious practice. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

If it is more likely that a mustahabb action will result in evil consequences, it is no longer mustahabb. Therefore a number of the fuqaha’ were of the view that some mustahabb actions should be abandoned if they have become symbols of the Raafidis (the Shi‘ah), because this does not mean that an obligatory duty is being abandoned. Rather doing that means that one is resembling them, and in that case it becomes difficult to distinguish between a Sunni and a Raafidi (Shi‘i). The interests served by being distinct from them, for the purpose of shunning them and differing from them, is greater than the interests served by doing this mustahabb action.

End quote from Minhaaj as-Sunnah an-Nabawiyyah (4/154) 

Shaykh Muhammad ibn Ibraaheem (may Allah have mercy on him) said: 

Some of the scholars emphatically disallowed resembling the followers of innovation in that which has become their symbols or slogans, even if it is Sunnah in principle. Both groups are agreed that it is not allowed to resemble the followers of innovation in that which is a symbol or slogan for them.

End quote from Fataawa wa Rasaa’il Muhammad ibn Ibraaheem (6/202) 

See also the answer to question no. 27237 and 6745 

Thirdly: 

The questioner asks whether it is acceptable, after reciting as-salaah al-Ibraaheemiyyah (“durood sharif”) in the final tashahhud, to recite this du‘aa’ only, followed immediately by the salaam, with no other du‘aa’ in between. 

If what he means by du‘aa’ here is this du‘aa’ that is known as the du‘aa’ of Kumayl ibn Ziyaad, then we have stated above that this is not acceptable and is in fact not allowed. 

But if what he means is to ask about the ruling on saying the salaam immediately after finishing as-salaah al-Ibraaheemiyyah, without saying any du‘aa’, then it is well known that saying du‘aa’ in the final tashahhud, after sending blessings upon the Prophet (blessings and peace of Allah be upon him) and before saying the salaam, is Sunnah but not obligatory. So it is permissible for the worshipper to say the salaam straight away, without saying du‘aa’. 

It says in al-Mawsoo‘ah al-Fiqhiyyah (27/98): 

It is Sunnah for the worshipper, after reciting the final tashahhud, to offer any du‘aa’ he wants, because the Prophet (blessings and peace of Allah be upon him) said: “When one of you sits during the prayer, let him say ‘At-tahiyyaatu Lillah…’ until the end, then let him ask Allah for whatever he wants or likes.” 

According to a report narrated by al-Bukhaari: “Then let him choose whatever du‘aa’ he likes, and say it.” According to another report, narrated by Muslim, he said: “Then after that let him ask for whatever he wants.”

End quote. 

It says in Asna al-Mataalib (1/166): 

“It is mustahabb to say du‘aa’ after that” means after sending blessings upon him and his family in the final tashahhud “as he wants” of matters of this world and of the Hereafter. End quote. 

Based on that, if the worshipper only sends blessings upon the Prophet (blessings and peace of Allah be upon him) then says the tasleem, and does not say du‘aa’ for anything, there is nothing wrong with that, but he is neglecting a Sunnah. 

Before saying the salaam, it is confirmed that one should seek refuge with Allah from four things: from the punishment of Hell, from the punishment of the grave, from the trials of life and death, and from the fitnah of the false messiah, the Dajjaal, because the Prophet (blessings and peace of Allah be upon him) enjoined that, according to a report narrated by Muslim (588) from Abu Hurayrah, who said: “When one of you has finished the final tashahhud, let him seek refuge with Allah from four things: from the punishment of Hell, from the punishment of the grave, from the trials of life and death, and from the evil of the Dajjaal.” 

An-Nawawi (may Allah have mercy on him) said: This clearly indicates that this is mustahabb in the final tashahhud. End quote. 

There are other du‘aa’s which it is also mustahabb for the worshipper to say after finishing the final tashahhud. For more information, please see the answer to question no. 5236.

And Allah knows best.