Praise be to Allah.
It is not permissible for anyone to pray istikhaarah on behalf of someone else.
It says in Liqa’ al-Baab al-Maftooh, by Shaykh Ibn ‘Uthaymeen (no. 89): Istikhaarah can only be done by the person who wants to do something or is thinking of doing it. It is not valid to pray istikhaarah on behalf of another person, even if he delegates him to do that and says: Pray istikhaarah to Allah for me (and ask Him to guide me concerning this matter), because the Messenger (blessings and peace of Allah be upon him) said: “‘If any one of you is deliberating about a decision he has to make, then let him pray two rak‘ahs…” By the same token, if two people enter the mosque and one of them says to the other: Pray two rak‘ahs for me to ‘greet the mosque’ (tahiyyat al-masjid), and I am going to sit down, that is not valid. Istikhaarah prayer is connected to the person who is seeking guidance concerning the thing he wants to do. End quote.
And Allah knows best.