Answer

In the Name of Allah, Most Gracious, Most Merciful. 

All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.

Answering your question, Dar Al-Ifta Al-Misriyyah, states:

It is permissible to offer the istikharah prayer before or after the witr prayer as it is permissible at any time provided it is not a time when prayer is disliked.

Almighty Allah knows best.

Source: Dar Al-Ifta Al-Misriyyah