What is prescribed with regard to duaa' al-istikhaarah is that it should be said after finishing the prayer. This is the view of the majority of scholars.
It says in al-Mawsooah al-Fiqhiyyah (3/245): The Hanafis, Maalikis, Shaafais and Hanbalis said: The duaa' should come immediately after the prayer. This is in accordance with what is mentioned in the text of the hadeeth from the Messenger of Allah (blessings and peace of Allah be upon him). End quote.
Shaykh Ibn Baaz (may Allah have mercy on him) said: What is prescribed for the Muslim, when he offers salaat al-istikhaarah, is to offer the duaa' after saying the salaam at the end of the prayer, because the Prophet (blessings and peace of Allah be upon him) said: If any one of you is concerned about a decision he has to make, then let him pray two rakahs of non-obligatory prayer, then say: Allaahumma inni astakheeruka bi ilmikaâ¦ (O Allaah, I seek Your guidance [in making a choice] by virtue of Your knowledgeâ¦)
This indicates that the duaa' should come after saying the salaam at the end of the prayer.
End quote from Majmoo al-Fataawa, 11/389
The scholars of the Standing Committee were asked: Does the duaa' of istikhaarah come before the tasleem or after saying the tasleem and finishing the prayer?
They replied: The duaa' of istikhaarah comes after the tasleem of salaat al- istikhaarah. End quote.
Shaykh Ibn Uthaymeen (may Allah have mercy on him) said: The duaa' of istikhaarah comes after the salaam, because the Prophet (blessings and peace of Allah be upon him) said: Let him pray two rakahs then let him sayâ¦ and he mentioned the duaa'.
End quote from Liqa' al-Baab al-Maftooh, no. 20
And Allah knows best.
Reproduced from Islam QA