How to Increase Provision
Question

“You pray two Rak`ahs, reciting in each Rak`ah Al-Hamd (i.e., Al-Fatihah) once and At-Tawhid (i.e., Al-Ikhlas) once, making the bowing and prostration lengthy. After finishing the prayer, say: ‘O Most Glorious, O One, O Most Generous, I turn to You by virtue of Muhammad Your Prophet, the Prophet of mercy, (blessings of Allah be upon him and his family); O Muhammad, O Messenger of Allah, I turn by virtue of you to Allah, my Lord and your Lord, the Lord of all things. I ask you, O Allah, to send blessings upon Muhammad and the members of his household, and I ask You for a breath of mercy from You, quick relief, and abundant provision, so that I may put my affairs in order, pay off my debts and support my dependents.’” Is this Hadith authentic?
Praise be to Allah.Is there a specific Du`a to increase provision?
In the authentic Sunnah there is no known prayer specifically for asking for increased provision. The prayer described in the question with this Du`a (supplication) is an innovated prayer; it comes under the heading of prescribing in religion something that Allah has not prescribed, and introducing innovation (Bid`ah) that is prohibited. 
Ibn Kathir (may Allah have mercy on him) said: 
“Ahl As-Sunnah wal-Jama‘ah consider any action or word that is not proven from the Companions to be an innovation (Bid`ah), because if it were something good, they would have done it before us. They did not omit any good attribute but they hastened to do it or attain it.” (Tafsir Ibn Kathir, 7/278-279)
Shaykh Salih Al-Fawzan (may Allah preserve him) said: 
“The innovations that have been introduced in the area of worship nowadays are many. But the basic principle with regard to acts of worship is Tawqif [i.e., they can only be known through divine Revelation and sound texts of Hadith, with no room for personal opinion], so no acts of worship are prescribed except on the basis of evidence. Anything for which there is no evidence is an innovation (Bid`ah), because the Prophet (blessings and peace of Allah be upon him) said: “Whoever does an action that is not part of this matter of ours will have it rejected.” (Al-Bukhari and Muslim). The acts of worship that are done nowadays for which there is no evidence are very many." (Kitab At-Tawhid, p. 160 )
Is it permissible to call upon the Messenger of Allah?
The words of the worshipper in this Du`a after this innovated prayer, “I turn to You by virtue of Muhammad Your Prophet , the Prophet of mercy, (blessings of Allah be upon him and his family); O Muhammad, O Messenger of Allah, I turn by virtue of you to Allah…” are words that are not permissible, and come under the heading of innovated Tawassul (means of seeking to draw closer to Allah) that is forbidden. 
Anyone who calls upon the Messenger of Allah (blessings and peace of Allah be upon him) after his death , or who calls upon anyone else among the dead to ward off harm or bring benefits has committed major Shirk (associating partners with Allah) that puts one beyond the pale of Islam, and he has to repent to Allah, may He be Exalted. 
How to increase provision in Islam
There are some means of increasing provision that are prescribed in Islam, which we shall highlight here, so as to adopt the means that are prescribed and warn against innovations in religion. These include: 

Istighfar (praying for forgiveness): Allah, may He be exalted, says (interpretation of the meaning):

“I said (to them): Ask forgiveness from your Lord; Verily, He is Oft-Forgiving; He will send rain to you in abundance; And give you increase in wealth and children, and bestow on you gardens and bestow on you rivers.” [Nuh 71:10-12] 

Upholding ties of kinship: Al-Bukhari (2067) and Muslim (2557) narrated from Anas ibn Malik (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever would like his provision to be increased and his life to be extended , should uphold the ties of kinship.” 

An-Nawawi (may Allah have mercy on him) said: 
“The term ‘His provision to be increased’ means to be expanded and made abundant or, it was said, to be blessed (Barakah).”

Giving a great deal of charity: Allah, may He be Exalted, says (interpretation of the meaning): 

“Say: Truly, my Lord enlarges the provision for whom He wills of His slaves, and (also) restricts (it) for him, and whatsoever you spend of anything (in Allah’s Cause), He will replace it. And He is the Best of providers.” [Saba’ 34:39] 
Muslim (2588) narrated from Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Charity does not decrease wealth.” 
An-Nawawi (may Allah have mercy on him) said: 
“The scholars mentioned two meanings of this Hadith, one of which is that (the wealth) will be blessed (as a result of giving charity ) and harm will be warded off from it, so the apparent decrease will be compensated for by means of hidden blessing. This is something that is well known from experience. The second is that even if it appears to be decreased outwardly, there will be compensation for that in the reward that results from it, and it will be increased manifold.” 

Being mindful of Allah and fearing Him: Allah, may He be exalted, says (interpretation of the meaning):

“And whosoever fears Allah and keeps his duty to Him, He will make a way for him to get out (from every difficulty). And He will provide him from (sources) he never could imagine.” [At-Talaq 65:2-3] 

Performing Hajj and `Umrah often, following one with the other: At-Tirmidhi (810) narrated that `Abdullah ibn Mas`ud (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Make the Hajj and `Umrah follow each other closely, for they remove poverty and sins as the bellows removes the dross of iron, gold and silver, and an accepted Hajj brings no less a reward than Paradise.” (It was classed as authentic by Al-Albani) 
Du`a (supplication) : It was narrated by Ibn Majah (925) from Umm Salamah (may Allah be pleased with her) that the Messenger of Allah (blessings and peace of Allah be upon him) used to say, after he said the Salam at the end of Fajr prayer: “Allahumma inni as’aluka `ilman nafi`an, wa rizqan tayyiban, wa `amalan mutaqabbalan (O Allah, I ask you for beneficial knowledge, good (lawful) provision, and accepted good deeds).” (Classed as authentic by Al-Albani in Sahih Ibn Majah) 

And Allah knows best.