When should the du‘aa’ be offered in salaat al-istikhaarah?

What is prescribed with regard to du‘aa’ 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-Mawsoo‘ah al-Fiqhiyyah (3/245): The
Hanafis, Maalikis, Shaafa‘is and Hanbalis said: The du‘aa’ 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 du‘aa’ 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 rak‘ahs
of non-obligatory prayer, then say: Allaahumma inni astakheeruka bi
‘ilmika… (O Allaah, I seek Your guidance [in making a choice] by virtue
of Your knowledge…)”

This indicates that the du‘aa’ 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
du‘aa’ of istikhaarah come before the tasleem or after saying the tasleem
and finishing the prayer? 

They replied: The du‘aa’ of istikhaarah comes after the
tasleem of salaat al- istikhaarah. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: The
du‘aa’ of istikhaarah comes after the salaam, because the Prophet (blessings
and peace of Allah be upon him) said: “Let him pray two rak‘ahs then let him
say…” and he mentioned the du‘aa’. 

End quote from Liqa’ al-Baab al-Maftooh, no. 20 

And Allah knows best.